From 99e0d466401e9940febf4948376b6dadb32a2dc2 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 13:44:44 +0100
Subject: [PATCH 01/23] toronto

---
 properties/P000219.md | 13 +++++++++++++
 theorems/T000802.md   |  9 +++++++++
 theorems/T000803.md   |  9 +++++++++
 theorems/T000804.md   |  9 +++++++++
 4 files changed, 40 insertions(+)
 create mode 100644 properties/P000219.md
 create mode 100644 theorems/T000802.md
 create mode 100644 theorems/T000803.md
 create mode 100644 theorems/T000804.md

diff --git a/properties/P000219.md b/properties/P000219.md
new file mode 100644
index 000000000..2ecd27f0d
--- /dev/null
+++ b/properties/P000219.md
@@ -0,0 +1,13 @@
+---
+uid: P000219
+name: Toronto
+refs:
+  - wikipedia: Toronto_space
+    name: Toronto space on Wikipedia
+  - zb : "1286.54032"
+    name : The Toronto Problem
+---
+
+Any subspace $Y \subseteq X$ with $|Y|=|X|$ is homeomorphic to $X$.
+
+In {{zb:1286.54032}} it is shown that under GCH, every {P3} Toronto space is {P52}.
diff --git a/theorems/T000802.md b/theorems/T000802.md
new file mode 100644
index 000000000..7c8dbdb74
--- /dev/null
+++ b/theorems/T000802.md
@@ -0,0 +1,9 @@
+---
+uid: T000802
+if:
+  - P000078: true
+then:
+  - P000219: true
+---
+
+For a finite space $X$, the only subspace with the same cardinality is $X$ itself, which is trivally homeomorphic to $X$.
diff --git a/theorems/T000803.md b/theorems/T000803.md
new file mode 100644
index 000000000..781215a93
--- /dev/null
+++ b/theorems/T000803.md
@@ -0,0 +1,9 @@
+---
+uid: T000803
+if:
+  - P000052: true
+then:
+  - P000137: true
+---
+
+Let $Y\subset X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.
diff --git a/theorems/T000804.md b/theorems/T000804.md
new file mode 100644
index 000000000..f11a8f5bc
--- /dev/null
+++ b/theorems/T000804.md
@@ -0,0 +1,9 @@
+---
+uid: T000804
+if:
+  - P000222: true
+then:
+  - P000219: true
+---
+
+Let $Y\subset X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.

From 8fa07eb2bc590c3b82a5e38a2f01e8d6c0236829 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 16:35:52 +0100
Subject: [PATCH 02/23] remove typo

---
 properties/P000219.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/properties/P000219.md b/properties/P000219.md
index 2ecd27f0d..7d85b981a 100644
--- a/properties/P000219.md
+++ b/properties/P000219.md
@@ -4,8 +4,8 @@ name: Toronto
 refs:
   - wikipedia: Toronto_space
     name: Toronto space on Wikipedia
-  - zb : "1286.54032"
-    name : The Toronto Problem
+  - zb: "1286.54032"
+    name: The Toronto Problem
 ---
 
 Any subspace $Y \subseteq X$ with $|Y|=|X|$ is homeomorphic to $X$.

From d5aa980cf283791deda6d358818e2c7f87f7b724 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 18:09:40 +0100
Subject: [PATCH 03/23] conflict

---
 theorems/{T000802.md => T000805.md} | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename theorems/{T000802.md => T000805.md} (93%)

diff --git a/theorems/T000802.md b/theorems/T000805.md
similarity index 93%
rename from theorems/T000802.md
rename to theorems/T000805.md
index 7c8dbdb74..15ddcb68f 100644
--- a/theorems/T000802.md
+++ b/theorems/T000805.md
@@ -1,5 +1,5 @@
 ---
-uid: T000802
+uid: T000805
 if:
   - P000078: true
 then:

From 0633259a79916a3af2081db4b98c96fb5b09774a Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 18:10:54 +0100
Subject: [PATCH 04/23] conflict'

---
 theorems/{T000803.md => T000806.md} | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename theorems/{T000803.md => T000806.md} (91%)

diff --git a/theorems/T000803.md b/theorems/T000806.md
similarity index 91%
rename from theorems/T000803.md
rename to theorems/T000806.md
index 781215a93..b77f55455 100644
--- a/theorems/T000803.md
+++ b/theorems/T000806.md
@@ -1,5 +1,5 @@
 ---
-uid: T000803
+uid: T000806
 if:
   - P000052: true
 then:

From d04848064222a8597d4c43357615b2d8f41b24cc Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 18:11:35 +0100
Subject: [PATCH 05/23] conflict''

---
 theorems/T000806.md                 | 2 +-
 theorems/{T000804.md => T000807.md} | 0
 2 files changed, 1 insertion(+), 1 deletion(-)
 rename theorems/{T000804.md => T000807.md} (100%)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index b77f55455..3d2ac39ca 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -1,5 +1,5 @@
 ---
-uid: T000806
+uid: T000807
 if:
   - P000052: true
 then:
diff --git a/theorems/T000804.md b/theorems/T000807.md
similarity index 100%
rename from theorems/T000804.md
rename to theorems/T000807.md

From 5c3e7e48b0a9d75e11b2e8a65c18090073f6fdbc Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 18:18:29 +0100
Subject: [PATCH 06/23] add author

---
 properties/P000219.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/properties/P000219.md b/properties/P000219.md
index 7d85b981a..20f82f96b 100644
--- a/properties/P000219.md
+++ b/properties/P000219.md
@@ -5,7 +5,7 @@ refs:
   - wikipedia: Toronto_space
     name: Toronto space on Wikipedia
   - zb: "1286.54032"
-    name: The Toronto Problem
+    name: The Toronto Problem (W. R. Brian)
 ---
 
 Any subspace $Y \subseteq X$ with $|Y|=|X|$ is homeomorphic to $X$.

From 89759628153cfb3c1684d786e46af4518b748521 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 19:12:09 +0100
Subject: [PATCH 07/23] typo

---
 theorems/T000806.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index 3d2ac39ca..9d8d0f9c6 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -6,4 +6,4 @@ then:
   - P000137: true
 ---
 
-Let $Y\subset X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.
+Let $Y\subseteq X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.

From 94496b9fa68860b10d4c14210c3927ec3da80040 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 19:13:19 +0100
Subject: [PATCH 08/23] mistake in theorem statement

---
 theorems/T000806.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index 9d8d0f9c6..fcc14bd08 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -3,7 +3,7 @@ uid: T000807
 if:
   - P000052: true
 then:
-  - P000137: true
+  - P000219: true
 ---
 
 Let $Y\subseteq X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.

From bb012b841df5b3372eb240f33f17154c5ed905a8 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 19:14:30 +0100
Subject: [PATCH 09/23] hopefully now

---
 theorems/T000806.md | 2 +-
 theorems/T000807.md | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/theorems/T000806.md b/theorems/T000806.md
index fcc14bd08..335c9714d 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -1,5 +1,5 @@
 ---
-uid: T000807
+uid: T000806
 if:
   - P000052: true
 then:
diff --git a/theorems/T000807.md b/theorems/T000807.md
index f11a8f5bc..eb75535a7 100644
--- a/theorems/T000807.md
+++ b/theorems/T000807.md
@@ -1,5 +1,5 @@
 ---
-uid: T000804
+uid: T000807
 if:
   - P000222: true
 then:

From 069d4d9e82a35334ea13c1168771c49bdcf286ce Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Wed, 24 Dec 2025 20:21:43 +0100
Subject: [PATCH 10/23] removed -

---
 theorems/T000805.md | 4 ++--
 theorems/T000806.md | 4 ++--
 theorems/T000807.md | 4 ++--
 3 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/theorems/T000805.md b/theorems/T000805.md
index 15ddcb68f..a38e04884 100644
--- a/theorems/T000805.md
+++ b/theorems/T000805.md
@@ -1,9 +1,9 @@
 ---
 uid: T000805
 if:
-  - P000078: true
+  P000078: true
 then:
-  - P000219: true
+  P000219: true
 ---
 
 For a finite space $X$, the only subspace with the same cardinality is $X$ itself, which is trivally homeomorphic to $X$.
diff --git a/theorems/T000806.md b/theorems/T000806.md
index 335c9714d..e99cf3abe 100644
--- a/theorems/T000806.md
+++ b/theorems/T000806.md
@@ -1,9 +1,9 @@
 ---
 uid: T000806
 if:
-  - P000052: true
+  P000052: true
 then:
-  - P000219: true
+  P000219: true
 ---
 
 Let $Y\subseteq X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.
diff --git a/theorems/T000807.md b/theorems/T000807.md
index eb75535a7..b282553af 100644
--- a/theorems/T000807.md
+++ b/theorems/T000807.md
@@ -1,9 +1,9 @@
 ---
 uid: T000807
 if:
-  - P000222: true
+  P000222: true
 then:
-  - P000219: true
+  P000219: true
 ---
 
 Let $Y\subset X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.

From b238706bae2fd8e33bf8e59e3ca789207cc0627f Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sat, 27 Dec 2025 22:44:01 +0100
Subject: [PATCH 11/23] cut point

---
 theorems/{T000805.md => T000905.md} |  2 +-
 theorems/{T000806.md => T000906.md} |  2 +-
 theorems/{T000807.md => T000907.md} |  2 +-
 theorems/T000908.md                 |  9 +++++++++
 theorems/T000909.md                 | 12 ++++++++++++
 5 files changed, 24 insertions(+), 3 deletions(-)
 rename theorems/{T000805.md => T000905.md} (93%)
 rename theorems/{T000806.md => T000906.md} (91%)
 rename theorems/{T000807.md => T000907.md} (91%)
 create mode 100644 theorems/T000908.md
 create mode 100644 theorems/T000909.md

diff --git a/theorems/T000805.md b/theorems/T000905.md
similarity index 93%
rename from theorems/T000805.md
rename to theorems/T000905.md
index a38e04884..8cccedee8 100644
--- a/theorems/T000805.md
+++ b/theorems/T000905.md
@@ -1,5 +1,5 @@
 ---
-uid: T000805
+uid: T000905
 if:
   P000078: true
 then:
diff --git a/theorems/T000806.md b/theorems/T000906.md
similarity index 91%
rename from theorems/T000806.md
rename to theorems/T000906.md
index e99cf3abe..3b5250a42 100644
--- a/theorems/T000806.md
+++ b/theorems/T000906.md
@@ -1,5 +1,5 @@
 ---
-uid: T000806
+uid: T000906
 if:
   P000052: true
 then:
diff --git a/theorems/T000807.md b/theorems/T000907.md
similarity index 91%
rename from theorems/T000807.md
rename to theorems/T000907.md
index b282553af..e7e326dcb 100644
--- a/theorems/T000807.md
+++ b/theorems/T000907.md
@@ -1,5 +1,5 @@
 ---
-uid: T000807
+uid: T000907
 if:
   P000222: true
 then:
diff --git a/theorems/T000908.md b/theorems/T000908.md
new file mode 100644
index 000000000..29e3ce8af
--- /dev/null
+++ b/theorems/T000908.md
@@ -0,0 +1,9 @@
+---
+uid: T000908
+if:
+  P000129: true
+then:
+  P000219: true
+---
+
+Let $Y\subset X$ with $|Y|=|X|$. Then any bijection $Y \to X$ is a homeomorphism.
diff --git a/theorems/T000909.md b/theorems/T000909.md
new file mode 100644
index 000000000..95c3ed434
--- /dev/null
+++ b/theorems/T000909.md
@@ -0,0 +1,12 @@
+---
+uid: T000909
+if:
+  and:
+  - P000219: true
+  - P000204: true
+then:
+  P000078: true
+---
+
+Let $p$ be a cut point of $X$. If $X$ were infinite, $|X\setminus \{p\}|=|X|$, but they cannot be homeomorphic as $X$ is connected but $X \setminus \{p\}$ is not.
+ 
\ No newline at end of file

From a64e4949b96d811efd6babc60ab491d4ffae925a Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:11:25 +0100
Subject: [PATCH 12/23] two more theorems

---
 theorems/T000909.md |  1 -
 theorems/T000910.md | 16 ++++++++++++++++
 theorems/T000911.md | 16 ++++++++++++++++
 3 files changed, 32 insertions(+), 1 deletion(-)
 create mode 100644 theorems/T000910.md
 create mode 100644 theorems/T000911.md

diff --git a/theorems/T000909.md b/theorems/T000909.md
index 95c3ed434..25754ce73 100644
--- a/theorems/T000909.md
+++ b/theorems/T000909.md
@@ -9,4 +9,3 @@ then:
 ---
 
 Let $p$ be a cut point of $X$. If $X$ were infinite, $|X\setminus \{p\}|=|X|$, but they cannot be homeomorphic as $X$ is connected but $X \setminus \{p\}$ is not.
- 
\ No newline at end of file
diff --git a/theorems/T000910.md b/theorems/T000910.md
new file mode 100644
index 000000000..914f7ce45
--- /dev/null
+++ b/theorems/T000910.md
@@ -0,0 +1,16 @@
+---
+uid: T000910
+if:
+  and:
+  - P000219: true
+  - P000196: false
+  - P000129: false
+then:
+  P000002: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+---
+
+Follows from Theorem 6.1 in {{zb:1286.54032}}.
diff --git a/theorems/T000911.md b/theorems/T000911.md
new file mode 100644
index 000000000..222ae66af
--- /dev/null
+++ b/theorems/T000911.md
@@ -0,0 +1,16 @@
+---
+uid: T000911
+if:
+  and:
+  - P000219: true
+  - P000181: true
+  - P000129: false
+then:
+  P000196: false
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+---
+
+Follows from Corollary 6.2 in {{zb:1286.54032}}.

From 703cc4646342c67da61674ae3e67514a013ca3a8 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:17:51 +0100
Subject: [PATCH 13/23] fix wrong theorem

---
 theorems/T000911.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/theorems/T000911.md b/theorems/T000911.md
index 222ae66af..066256dba 100644
--- a/theorems/T000911.md
+++ b/theorems/T000911.md
@@ -6,7 +6,7 @@ if:
   - P000181: true
   - P000129: false
 then:
-  P000196: false
+  P000196: true
 refs:
   - zb: "1286.54032"
     name: The Toronto Problem (W. R. Brian)

From 48d85ed7b702be94a1a04a0e58d4c8daf9ab0212 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:28:33 +0100
Subject: [PATCH 14/23] typo

---
 theorems/T000910.md | 1 -
 theorems/T000911.md | 1 -
 2 files changed, 2 deletions(-)

diff --git a/theorems/T000910.md b/theorems/T000910.md
index 914f7ce45..4c1fea2f3 100644
--- a/theorems/T000910.md
+++ b/theorems/T000910.md
@@ -11,6 +11,5 @@ refs:
   - zb: "1286.54032"
     name: The Toronto Problem (W. R. Brian)
 ---
----
 
 Follows from Theorem 6.1 in {{zb:1286.54032}}.
diff --git a/theorems/T000911.md b/theorems/T000911.md
index 066256dba..c16966c1a 100644
--- a/theorems/T000911.md
+++ b/theorems/T000911.md
@@ -11,6 +11,5 @@ refs:
   - zb: "1286.54032"
     name: The Toronto Problem (W. R. Brian)
 ---
----
 
 Follows from Corollary 6.2 in {{zb:1286.54032}}.

From 4078a309a00c5d51736a1bb4fa8b610ad172c23e Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:43:57 +0100
Subject: [PATCH 15/23] no 911

---
 properties/P000223.md |  0
 theorems/T000911.md   | 15 ---------------
 2 files changed, 15 deletions(-)
 create mode 100644 properties/P000223.md
 delete mode 100644 theorems/T000911.md

diff --git a/properties/P000223.md b/properties/P000223.md
new file mode 100644
index 000000000..e69de29bb
diff --git a/theorems/T000911.md b/theorems/T000911.md
deleted file mode 100644
index c16966c1a..000000000
--- a/theorems/T000911.md
+++ /dev/null
@@ -1,15 +0,0 @@
----
-uid: T000911
-if:
-  and:
-  - P000219: true
-  - P000181: true
-  - P000129: false
-then:
-  P000196: true
-refs:
-  - zb: "1286.54032"
-    name: The Toronto Problem (W. R. Brian)
----
-
-Follows from Corollary 6.2 in {{zb:1286.54032}}.

From e0e44ce630cf9a9638a31bd9968d420575ed8544 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:45:15 +0100
Subject: [PATCH 16/23] test

---
 theorems/T000910.md | 15 ---------------
 1 file changed, 15 deletions(-)
 delete mode 100644 theorems/T000910.md

diff --git a/theorems/T000910.md b/theorems/T000910.md
deleted file mode 100644
index 4c1fea2f3..000000000
--- a/theorems/T000910.md
+++ /dev/null
@@ -1,15 +0,0 @@
----
-uid: T000910
-if:
-  and:
-  - P000219: true
-  - P000196: false
-  - P000129: false
-then:
-  P000002: true
-refs:
-  - zb: "1286.54032"
-    name: The Toronto Problem (W. R. Brian)
----
-
-Follows from Theorem 6.1 in {{zb:1286.54032}}.

From d2e9b2abd15b20ee684bd316cbd53356913acc9a Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 00:56:08 +0100
Subject: [PATCH 17/23] remove misplaced file

---
 properties/P000223.md |  0
 theorems/T000909.md   |  1 +
 theorems/T000910.md   | 15 +++++++++++++++
 theorems/T000911.md   | 15 +++++++++++++++
 4 files changed, 31 insertions(+)
 delete mode 100644 properties/P000223.md
 create mode 100644 theorems/T000910.md
 create mode 100644 theorems/T000911.md

diff --git a/properties/P000223.md b/properties/P000223.md
deleted file mode 100644
index e69de29bb..000000000
diff --git a/theorems/T000909.md b/theorems/T000909.md
index 25754ce73..95c3ed434 100644
--- a/theorems/T000909.md
+++ b/theorems/T000909.md
@@ -9,3 +9,4 @@ then:
 ---
 
 Let $p$ be a cut point of $X$. If $X$ were infinite, $|X\setminus \{p\}|=|X|$, but they cannot be homeomorphic as $X$ is connected but $X \setminus \{p\}$ is not.
+ 
\ No newline at end of file
diff --git a/theorems/T000910.md b/theorems/T000910.md
new file mode 100644
index 000000000..4c1fea2f3
--- /dev/null
+++ b/theorems/T000910.md
@@ -0,0 +1,15 @@
+---
+uid: T000910
+if:
+  and:
+  - P000219: true
+  - P000196: false
+  - P000129: false
+then:
+  P000002: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+Follows from Theorem 6.1 in {{zb:1286.54032}}.
diff --git a/theorems/T000911.md b/theorems/T000911.md
new file mode 100644
index 000000000..c16966c1a
--- /dev/null
+++ b/theorems/T000911.md
@@ -0,0 +1,15 @@
+---
+uid: T000911
+if:
+  and:
+  - P000219: true
+  - P000181: true
+  - P000129: false
+then:
+  P000196: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+Follows from Corollary 6.2 in {{zb:1286.54032}}.

From 730c233593b33b9ab0115a8409f06bf364b0eea6 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 02:09:42 +0100
Subject: [PATCH 18/23] add suggestions

---
 theorems/T000909.md | 2 +-
 theorems/T000910.md | 1 +
 theorems/T000911.md | 2 ++
 3 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/theorems/T000909.md b/theorems/T000909.md
index 95c3ed434..e6c1e8a9b 100644
--- a/theorems/T000909.md
+++ b/theorems/T000909.md
@@ -8,5 +8,5 @@ then:
   P000078: true
 ---
 
-Let $p$ be a cut point of $X$. If $X$ were infinite, $|X\setminus \{p\}|=|X|$, but they cannot be homeomorphic as $X$ is connected but $X \setminus \{p\}$ is not.
+Let $p$ be a cut point of $X$. If $X$ were infinite, $|X\setminus \{p\}|=|X|$, but they cannot be homeomorphic as $X$ is {P36} but $X \setminus \{p\}$ is not.
  
\ No newline at end of file
diff --git a/theorems/T000910.md b/theorems/T000910.md
index 4c1fea2f3..b30275214 100644
--- a/theorems/T000910.md
+++ b/theorems/T000910.md
@@ -5,6 +5,7 @@ if:
   - P000219: true
   - P000196: false
   - P000129: false
+  - P000078: false
 then:
   P000002: true
 refs:
diff --git a/theorems/T000911.md b/theorems/T000911.md
index c16966c1a..b00527b89 100644
--- a/theorems/T000911.md
+++ b/theorems/T000911.md
@@ -5,6 +5,8 @@ if:
   - P000219: true
   - P000181: true
   - P000129: false
+  - P000052: false
+  - P000222: false
 then:
   P000196: true
 refs:

From b6fa40a7621c13a1ecc1ea8ded28af497509a974 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 02:48:52 +0100
Subject: [PATCH 19/23] hausdorff theorems

---
 theorems/T000912.md | 15 +++++++++++++++
 theorems/T000913.md | 15 +++++++++++++++
 theorems/T000914.md | 15 +++++++++++++++
 theorems/T000915.md | 15 +++++++++++++++
 theorems/T000916.md | 17 +++++++++++++++++
 theorems/T000917.md | 15 +++++++++++++++
 theorems/T000918.md | 15 +++++++++++++++
 7 files changed, 107 insertions(+)
 create mode 100644 theorems/T000912.md
 create mode 100644 theorems/T000913.md
 create mode 100644 theorems/T000914.md
 create mode 100644 theorems/T000915.md
 create mode 100644 theorems/T000916.md
 create mode 100644 theorems/T000917.md
 create mode 100644 theorems/T000918.md

diff --git a/theorems/T000912.md b/theorems/T000912.md
new file mode 100644
index 000000000..cc4749bbc
--- /dev/null
+++ b/theorems/T000912.md
@@ -0,0 +1,15 @@
+---
+uid: T000912
+if:
+  and:
+  - P000219: true
+  - P000028: true
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Corollary 3.2 in {{zb:1286.54032}}.
diff --git a/theorems/T000913.md b/theorems/T000913.md
new file mode 100644
index 000000000..fc5c6d905
--- /dev/null
+++ b/theorems/T000913.md
@@ -0,0 +1,15 @@
+---
+uid: T000913
+if:
+  and:
+  - P000219: true
+  - P000154: true
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Corollary 3.4 in {{zb:1286.54032}}.
diff --git a/theorems/T000914.md b/theorems/T000914.md
new file mode 100644
index 000000000..50caa2dc2
--- /dev/null
+++ b/theorems/T000914.md
@@ -0,0 +1,15 @@
+---
+uid: T000914
+if:
+  and:
+  - P000219: true
+  - P000136: false
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Corollary 3.5 in {{zb:1286.54032}}.
diff --git a/theorems/T000915.md b/theorems/T000915.md
new file mode 100644
index 000000000..1ed45582c
--- /dev/null
+++ b/theorems/T000915.md
@@ -0,0 +1,15 @@
+---
+uid: T000915
+if:
+  and:
+  - P000219: true
+  - P000030: true
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Proposition 3.8 in {{zb:1286.54032}}.
diff --git a/theorems/T000916.md b/theorems/T000916.md
new file mode 100644
index 000000000..05a7b2fbd
--- /dev/null
+++ b/theorems/T000916.md
@@ -0,0 +1,17 @@
+---
+uid: T000916
+if:
+  and:
+  - P000219: true
+  - P000030: true
+  - P000003: true
+  - P000011: true
+  - P000019: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Proposition 3.11 in {{zb:1286.54032}}.
diff --git a/theorems/T000917.md b/theorems/T000917.md
new file mode 100644
index 000000000..0b8128e9f
--- /dev/null
+++ b/theorems/T000917.md
@@ -0,0 +1,15 @@
+---
+uid: T000917
+if:
+  and:
+  - P000219: true
+  - P000018: true
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Proposition 2.3 in {{zb:1286.54032}}.
diff --git a/theorems/T000918.md b/theorems/T000918.md
new file mode 100644
index 000000000..d1305032d
--- /dev/null
+++ b/theorems/T000918.md
@@ -0,0 +1,15 @@
+---
+uid: T000918
+if:
+  and:
+  - P000219: true
+  - P000180: false
+  - P000003: true
+then:
+  P000052: true
+refs:
+  - zb: "1286.54032"
+    name: The Toronto Problem (W. R. Brian)
+---
+
+See Proposition 2.3 in {{zb:1286.54032}}.

From 345266d09cfdf57e7024a05f706ea623d6d46397 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 03:02:50 +0100
Subject: [PATCH 20/23] update theorems

---
 theorems/T000913.md |  4 ++--
 theorems/T000916.md | 17 -----------------
 2 files changed, 2 insertions(+), 19 deletions(-)
 delete mode 100644 theorems/T000916.md

diff --git a/theorems/T000913.md b/theorems/T000913.md
index fc5c6d905..846fc8671 100644
--- a/theorems/T000913.md
+++ b/theorems/T000913.md
@@ -3,7 +3,7 @@ uid: T000913
 if:
   and:
   - P000219: true
-  - P000154: true
+  - P000093: false
   - P000003: true
 then:
   P000052: true
@@ -12,4 +12,4 @@ refs:
     name: The Toronto Problem (W. R. Brian)
 ---
 
-See Corollary 3.4 in {{zb:1286.54032}}.
+See the proof of Corollary 3.4 in {{zb:1286.54032}}.
diff --git a/theorems/T000916.md b/theorems/T000916.md
deleted file mode 100644
index 05a7b2fbd..000000000
--- a/theorems/T000916.md
+++ /dev/null
@@ -1,17 +0,0 @@
----
-uid: T000916
-if:
-  and:
-  - P000219: true
-  - P000030: true
-  - P000003: true
-  - P000011: true
-  - P000019: true
-then:
-  P000052: true
-refs:
-  - zb: "1286.54032"
-    name: The Toronto Problem (W. R. Brian)
----
-
-See Proposition 3.11 in {{zb:1286.54032}}.

From 80e033b84704c4d787cb95d538166d3e3e2d5673 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 03:12:55 +0100
Subject: [PATCH 21/23] improve thanks to yhx

---
 theorems/T000912.md | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/theorems/T000912.md b/theorems/T000912.md
index cc4749bbc..2f88779ac 100644
--- a/theorems/T000912.md
+++ b/theorems/T000912.md
@@ -3,13 +3,12 @@ uid: T000912
 if:
   and:
   - P000219: true
-  - P000028: true
   - P000003: true
 then:
-  P000052: true
+  P000167: true
 refs:
   - zb: "1286.54032"
     name: The Toronto Problem (W. R. Brian)
 ---
 
-See Corollary 3.2 in {{zb:1286.54032}}.
+Immediate consequence of Theorem 3.1 in {{zb:1286.54032}}.

From 1c6e93270183303a0589997b9a3100a98c0cb3a3 Mon Sep 17 00:00:00 2001
From: Felix Pernegger <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 11:07:04 +0100
Subject: [PATCH 22/23] Update theorems/T000913.md

Co-authored-by: yhx-12243 <yhx12243@gmail.com>
---
 theorems/T000913.md | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/theorems/T000913.md b/theorems/T000913.md
index 846fc8671..7cc3de723 100644
--- a/theorems/T000913.md
+++ b/theorems/T000913.md
@@ -3,10 +3,9 @@ uid: T000913
 if:
   and:
   - P000219: true
-  - P000093: false
   - P000003: true
 then:
-  P000052: true
+  P000093: true
 refs:
   - zb: "1286.54032"
     name: The Toronto Problem (W. R. Brian)

From 2e3ff154b3ae7fa9d42696e68a151b476cd42c59 Mon Sep 17 00:00:00 2001
From: Batixx <s59fpern@uni-bonn.de>
Date: Sun, 28 Dec 2025 11:08:12 +0100
Subject: [PATCH 23/23] remove redundant

---
 theorems/T000915.md | 15 ---------------
 theorems/T000917.md | 15 ---------------
 2 files changed, 30 deletions(-)
 delete mode 100644 theorems/T000915.md
 delete mode 100644 theorems/T000917.md

diff --git a/theorems/T000915.md b/theorems/T000915.md
deleted file mode 100644
index 1ed45582c..000000000
--- a/theorems/T000915.md
+++ /dev/null
@@ -1,15 +0,0 @@
----
-uid: T000915
-if:
-  and:
-  - P000219: true
-  - P000030: true
-  - P000003: true
-then:
-  P000052: true
-refs:
-  - zb: "1286.54032"
-    name: The Toronto Problem (W. R. Brian)
----
-
-See Proposition 3.8 in {{zb:1286.54032}}.
diff --git a/theorems/T000917.md b/theorems/T000917.md
deleted file mode 100644
index 0b8128e9f..000000000
--- a/theorems/T000917.md
+++ /dev/null
@@ -1,15 +0,0 @@
----
-uid: T000917
-if:
-  and:
-  - P000219: true
-  - P000018: true
-  - P000003: true
-then:
-  P000052: true
-refs:
-  - zb: "1286.54032"
-    name: The Toronto Problem (W. R. Brian)
----
-
-See Proposition 2.3 in {{zb:1286.54032}}.