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Non T1 (P2) Toronto (P219) spaces #1565

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Merged
prabau merged 3 commits into from
Jan 1, 2026
Merged

Non T1 (P2) Toronto (P219) spaces #1565

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c2cede9
Non T1 Toronto spaces
felixpernegger Dec 29, 2025
193453e
indiscrete not needed
felixpernegger Dec 31, 2025
c5cd793
P196 additional condition
prabau Jan 1, 2026
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1 change: 1 addition & 0 deletions properties/P000196.md
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Expand Up @@ -13,6 +13,7 @@ Every subspace is connected.
This is equivalent to each of the following:

- The open sets are totally ordered by inclusion.
- There is a basis of open sets that is totally ordered by inclusion.
- The closed sets are totally ordered by inclusion.
- The specialization preorder is total.

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15 changes: 15 additions & 0 deletions theorems/T000819.md
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@@ -0,0 +1,15 @@
---
uid: T000819
if:
and:
- P000219: true
- P000002: false
- P000078: false
then:
P000196: true
refs:
- zb: "1286.54032"
name: The Toronto Problem (W. R. Brian)
---

Follows from Theorem 6.1 in {{zb:1286.54032}}.