Question

Where does "A family of compact sets with the finite intersection property has nonempty intersection" lie between $T_1$ and $T_2$?

score 229 · Answer 1 · 2023-12-10 01:46:31

229

Views

Where does "A family of compact sets with the finite intersection property has nonempty intersection" lie between $T_1$ and $T_2$?

Published on 10 Dec 2023 - 1:46

score 92 · Answer 2 · 2024-01-01 16:49:11

92

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Is the Alexandrov extension the unique $k_2$-Hausdorff one-point compactification of a KC space?

Published on 01 Jan 2024 - 16:49

score 71 · Answer 3 · 2024-01-07 09:32:22

71

Views

Countably compact $T_0$ space $S$ such that for all $X\subseteq S$ and every $p\in X'$, there exists an open set $O$ such that ...

Published on 07 Jan 2024 - 9:32

score 175 · Answer 4 · 2024-01-11 18:28:51

175

Views

How to prove this topological lemma?

Published on 11 Jan 2024 - 18:28

score 92 · Answer 5 · 2024-01-13 21:12:37

92

Views

How to limit deformation retraction to a subset in perfectly normal spaces?

Published on 13 Jan 2024 - 21:12

score 196 · Answer 6 · 2024-01-14 05:11:10

196

Views

Can a Fréchet-Urysohn hemicompact Hausdorff space fail to be locally compact?

Published on 14 Jan 2024 - 5:11

score 48 · Answer 7 · 2024-01-20 12:51:00

48

Views

When can we upgrade $k$-space definitions under a local Hausdorff condition?

Published on 20 Jan 2024 - 12:51

score 164 · Answer 8 · 2024-01-22 01:09:14

164

Views

Is a locally compact weak Hausdorff space Hausdorff?

Published on 22 Jan 2024 - 1:09

score 59 · Answer 9 · 2026-03-26 11:16:51

59

Views

Does a separable, $US$, sequential space have cardinality at most the continuum?

Published on 26 Mar 2026 - 11:16

score 67 · Answer 10 · 2024-01-27 08:04:58

67

Views

Quotients of $T_3$ spaces need not be regular.

Published on 27 Jan 2024 - 8:04

score 44 · Answer 11 · 2024-01-28 22:09:31

44

Views

All separation axioms are preserved under disjoint union?

Published on 28 Jan 2024 - 22:09

score 60 · Answer 12 · 2024-01-29 00:27:41

60

Views

What separation properties are guaranteed in sequentially discrete spaces?

Published on 29 Jan 2024 - 0:27

score 118 · Answer 13 · 2026-02-23 04:35:49

118

Views

Fully normal implies paracompact without a $T_1$ assumption?

Published on 23 Feb 2026 - 4:35

score 87 · Answer 14 · 2026-03-25 20:57:58

87

Views

Necessity of Hausdorff-ness in "continuous function determined by its values on a dense subset"

Published on 25 Mar 2026 - 20:57

score 104 · Answer 15 · 2024-03-01 14:27:32

104

Views

Different Hausdorff topologies with the same continuous mappings

Published on 01 Mar 2024 - 14:27

List Question

Where does "A family of compact sets with the finite intersection property has nonempty intersection" lie between $T_1$ and $T_2$?

Is the Alexandrov extension the unique $k_2$-Hausdorff one-point compactification of a KC space?

Countably compact $T_0$ space $S$ such that for all $X\subseteq S$ and every $p\in X'$, there exists an open set $O$ such that ...

How to prove this topological lemma?

How to limit deformation retraction to a subset in perfectly normal spaces?

Can a Fréchet-Urysohn hemicompact Hausdorff space fail to be locally compact?

When can we upgrade $k$-space definitions under a local Hausdorff condition?

Is a locally compact weak Hausdorff space Hausdorff?

Does a separable, $US$, sequential space have cardinality at most the continuum?

Quotients of $T_3$ spaces need not be regular.

All separation axioms are preserved under disjoint union?

What separation properties are guaranteed in sequentially discrete spaces?

Fully normal implies paracompact without a $T_1$ assumption?

Necessity of Hausdorff-ness in "continuous function determined by its values on a dense subset"

Different Hausdorff topologies with the same continuous mappings

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