diff --git a/spaces/S000036/properties/P000151.md b/spaces/S000036/properties/P000151.md new file mode 100644 index 0000000000..8cb181165a --- /dev/null +++ b/spaces/S000036/properties/P000151.md @@ -0,0 +1,7 @@ +--- +space: S000036 +property: P000151 +value: true +--- + +In the first round, after Player I picked some open cover, Player II can then pick a cocountable neighborhood $U$ of the point $\omega_1 \in X$. Choose an enumeration $X\setminus U = \{x_1,x_2,\dots\}$. Player II then has a winning strategy by picking a neighborhood of $x_n$ in the $n+1$-th step of the game. diff --git a/spaces/S000141/properties/P000020.md b/spaces/S000141/properties/P000020.md deleted file mode 100644 index 31f133c40d..0000000000 --- a/spaces/S000141/properties/P000020.md +++ /dev/null @@ -1,7 +0,0 @@ ---- -space: S000141 -property: P000020 -value: true ---- - -$X$ the union of its two {P20} subspaces $\omega_1$ and $1+\omega^*$: {S35|P20} and {S20|P20}. diff --git a/spaces/S000141/properties/P000081.md b/spaces/S000141/properties/P000081.md deleted file mode 100644 index 7daaefb561..0000000000 --- a/spaces/S000141/properties/P000081.md +++ /dev/null @@ -1,7 +0,0 @@ ---- -space: S000141 -property: P000081 -value: false ---- - -{P81} is a hereditary property. The space contains the subspace $\omega_1+1$, and {S36|P81}. diff --git a/spaces/S000141/properties/P000103.md b/spaces/S000141/properties/P000103.md new file mode 100644 index 0000000000..941f51b49a --- /dev/null +++ b/spaces/S000141/properties/P000103.md @@ -0,0 +1,7 @@ +--- +space: S000141 +property: P000103 +value: false +--- + +$X$ contains {S36} as a subspace, and {S36|P103}. diff --git a/spaces/S000141/properties/P000126.md b/spaces/S000141/properties/P000126.md deleted file mode 100644 index 1f097f48b1..0000000000 --- a/spaces/S000141/properties/P000126.md +++ /dev/null @@ -1,8 +0,0 @@ ---- -space: S000141 -property: P000126 -value: false ---- - -This space contains {S35} as a subspace, and {S35|P126}. -Therefore {S141} is not {P126}. diff --git a/spaces/S000141/properties/P000151.md b/spaces/S000141/properties/P000151.md new file mode 100644 index 0000000000..4f118c0d84 --- /dev/null +++ b/spaces/S000141/properties/P000151.md @@ -0,0 +1,7 @@ +--- +space: S000141 +property: P000151 +value: true +--- + +Similar to {S36|P151}.