From d411da9d61c82366431d16d9e4f3355dd1cff67c Mon Sep 17 00:00:00 2001 From: Batixx Date: Thu, 25 Dec 2025 13:44:47 +0100 Subject: [PATCH 1/3] complete s31 --- properties/P000210.md | 5 +++++ properties/P000211.md | 5 +++++ properties/P000212.md | 5 +++++ properties/P000213.md | 5 +++++ properties/P000214.md | 5 +++++ spaces/S000031/properties/P000036.md | 2 +- spaces/S000031/properties/P000084.md | 2 +- spaces/S000031/properties/P000138.md | 2 +- spaces/S000031/properties/P000214.md | 7 +++++++ spaces/S000031/properties/P000216.md | 7 +++++++ 10 files changed, 42 insertions(+), 3 deletions(-) create mode 100644 spaces/S000031/properties/P000214.md create mode 100644 spaces/S000031/properties/P000216.md diff --git a/properties/P000210.md b/properties/P000210.md index 3f21fdc5fd..7ae5540a4a 100644 --- a/properties/P000210.md +++ b/properties/P000210.md @@ -30,3 +30,8 @@ as done in {{zb:0774.54019}}. The $\alpha_i$ properties for $i = 1, 2, 3, 4$ (sometimes called "sheaf amalgamation properties") are due to Arkhangel'skii ({{zb:0275.54004}}). + +---- +#### Meta-properties + +- This property is hereditary. diff --git a/properties/P000211.md b/properties/P000211.md index 5ba213be72..45bdf65186 100644 --- a/properties/P000211.md +++ b/properties/P000211.md @@ -29,3 +29,8 @@ One can also phrase the definition in terms of (injective) sequences of elements as done in {{zb:0774.54019}}. This property was introduced by Nyikos in {{zb:0774.54019}}. + +---- +#### Meta-properties + +- This property is hereditary. diff --git a/properties/P000212.md b/properties/P000212.md index e904042ba3..0489e2f72f 100644 --- a/properties/P000212.md +++ b/properties/P000212.md @@ -29,3 +29,8 @@ as done in {{zb:0774.54019}}. The $\alpha_i$ properties for $i = 1, 2, 3, 4$ (sometimes called "sheaf amalgamation properties") are due to Arkhangel'skii ({{zb:0275.54004}}). + +---- +#### Meta-properties + +- This property is hereditary. diff --git a/properties/P000213.md b/properties/P000213.md index 89e031feac..8e5da280e1 100644 --- a/properties/P000213.md +++ b/properties/P000213.md @@ -29,3 +29,8 @@ as done in {{zb:0774.54019}}. The $\alpha_i$ properties for $i = 1, 2, 3, 4$ (sometimes called "sheaf amalgamation properties") are due to Arkhangel'skii ({{zb:0275.54004}}). + +---- +#### Meta-properties + +- This property is hereditary. diff --git a/properties/P000214.md b/properties/P000214.md index 394872eef2..47a4b1e41b 100644 --- a/properties/P000214.md +++ b/properties/P000214.md @@ -29,3 +29,8 @@ as done in {{zb:0774.54019}}. The $\alpha_i$ properties for $i = 1, 2, 3, 4$ (sometimes called "sheaf amalgamation properties") are due to Arkhangel'skii ({{zb:0275.54004}}). + +---- +#### Meta-properties + +- This property is hereditary. diff --git a/spaces/S000031/properties/P000036.md b/spaces/S000031/properties/P000036.md index d07717707c..f960a78437 100644 --- a/spaces/S000031/properties/P000036.md +++ b/spaces/S000031/properties/P000036.md @@ -7,4 +7,4 @@ refs: name: General Topology (Willard) --- -The space {S29} has the {P36} property. And the property is preserved by products, as shown in Theorem 26.10 of {{zb:1052.54001}}. +$X$ is the square of {S29} and {S29|P36}. diff --git a/spaces/S000031/properties/P000084.md b/spaces/S000031/properties/P000084.md index 01947370d4..de90eb11b0 100644 --- a/spaces/S000031/properties/P000084.md +++ b/spaces/S000031/properties/P000084.md @@ -4,4 +4,4 @@ property: P000084 value: false --- -It has {S29} as a subspace and {S29|P84}. +$X$ has {S29} as a subspace and {S29|P84}. diff --git a/spaces/S000031/properties/P000138.md b/spaces/S000031/properties/P000138.md index 85820d1516..970e43d412 100644 --- a/spaces/S000031/properties/P000138.md +++ b/spaces/S000031/properties/P000138.md @@ -4,4 +4,4 @@ property: P000138 value: false --- -Since {S29|P138}, there are uncountably many continuous maps $X\to X$. +Since {S29|P138}, there are uncountably many continuous maps $X\to X$ (by first projecting to the first component). diff --git a/spaces/S000031/properties/P000214.md b/spaces/S000031/properties/P000214.md new file mode 100644 index 0000000000..12ae397f05 --- /dev/null +++ b/spaces/S000031/properties/P000214.md @@ -0,0 +1,7 @@ +--- +space: S000031 +property: P000214 +value: false +--- + +$X$ has {S29} as a subspace and {S29|P214}. diff --git a/spaces/S000031/properties/P000216.md b/spaces/S000031/properties/P000216.md new file mode 100644 index 0000000000..dab3e34cea --- /dev/null +++ b/spaces/S000031/properties/P000216.md @@ -0,0 +1,7 @@ +--- +space: S000031 +property: P000216 +value: false +--- + +$X$ has {S29} as a subspace and {S29|P216}. From e23751d838a9fde83c4924074d5076005fb62ca3 Mon Sep 17 00:00:00 2001 From: Batixx Date: Thu, 25 Dec 2025 14:00:40 +0100 Subject: [PATCH 2/3] remove redundant --- spaces/S000031/properties/P000036.md | 10 ---------- spaces/S000031/properties/P000100.md | 12 ------------ 2 files changed, 22 deletions(-) delete mode 100644 spaces/S000031/properties/P000036.md delete mode 100644 spaces/S000031/properties/P000100.md diff --git a/spaces/S000031/properties/P000036.md b/spaces/S000031/properties/P000036.md deleted file mode 100644 index f960a78437..0000000000 --- a/spaces/S000031/properties/P000036.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -space: S000031 -property: P000036 -value: true -refs: -- zb: "1052.54001" - name: General Topology (Willard) ---- - -$X$ is the square of {S29} and {S29|P36}. diff --git a/spaces/S000031/properties/P000100.md b/spaces/S000031/properties/P000100.md deleted file mode 100644 index 5ab9bac341..0000000000 --- a/spaces/S000031/properties/P000100.md +++ /dev/null @@ -1,12 +0,0 @@ ---- -space: S000031 -property: P000100 -value: false -refs: -- mathse: 632320 - name: Weak Hausdorff space not KC ---- - -The diagonal $\Delta=\{(x,x):x\in\mathbb Q^*\}\subseteq X$ is homeomorphic to $\mathbb Q^*$ ({S29}), which is {P16}. But it is not closed in $X=\mathbb Q^*\times\mathbb Q^*$ since $\mathbb Q^*$ is not {P3}. This shows that $X$ is not {P100}. - -See {{mathse:632320}}. From a6db66a4f3932134cb6399086ec847fc390a92bf Mon Sep 17 00:00:00 2001 From: Moniker1998 <88507423+Moniker1998@users.noreply.github.com> Date: Thu, 25 Dec 2025 22:25:50 +0100 Subject: [PATCH 3/3] Update spaces/S000031/properties/P000138.md Co-authored-by: Felix Pernegger --- spaces/S000031/properties/P000138.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/spaces/S000031/properties/P000138.md b/spaces/S000031/properties/P000138.md index 970e43d412..d32b63cfc5 100644 --- a/spaces/S000031/properties/P000138.md +++ b/spaces/S000031/properties/P000138.md @@ -4,4 +4,5 @@ property: P000138 value: false --- -Since {S29|P138}, there are uncountably many continuous maps $X\to X$ (by first projecting to the first component). +For any continuous $f:\mathbb{Q}^*\to \mathbb{Q}^*$, $f\times f: X \to X$ is also continuous. +As {S29|P138}, this gives us uncountably many continuous self-maps of $X$.