Question

The Hausdorff property versus closedness of the diagonal in the context of convergence spaces

score 231 · Answer 1 · 2017-07-28 06:40:25

231

Views

The Hausdorff property versus closedness of the diagonal in the context of convergence spaces

Published on 28 Jul 2017 - 6:40

score 249 · Answer 2 · 2026-03-25 20:15:52

249

Views

$X$ compact Hausdorff space whose diagonal is a zero set: prove that the diagonal in $X \times X$ is a $G_{\delta}$ -set

Published on 25 Mar 2026 - 20:15

score 676 · Answer 3 · 2017-08-01 06:05:46

676

Views

Epimorphisms in the category of separated schemes

Published on 01 Aug 2017 - 6:05

score 456 · Answer 4 · 2026-03-25 22:09:47

456

Views

Prove that a countably compact, first countable $T_{2}$ space is regular.

Published on 25 Mar 2026 - 22:09

score 430 · Answer 5 · 2017-08-06 21:56:00

430

Views

A continuous open image of completely regular space need not be completely regular

Published on 06 Aug 2017 - 21:56

score 1.8k · Answer 6 · 2017-08-18 09:45:00

1.8k

Views

Showing that if $x$ is a limit point of $A$ in a $T_1$ space, then every neighborhoood of $x$ contains infinitely many points of $A$?

Published on 18 Aug 2017 - 9:45

score 46 · Answer 7 · 2017-08-22 14:44:06

46

Views

Literature references for the evident 'arc'-version of 'paths in a space compose'.

Published on 22 Aug 2017 - 14:44

score 3.1k · Answer 8 · 2017-08-22 21:50:52

3.1k

Views

Pre-image of Hausdorff space is Hausdorff

Published on 22 Aug 2017 - 21:50

score 81 · Answer 9 · 2017-08-28 17:47:59

81

Views

Does an homeomorphism preserve $T_1$?

Published on 28 Aug 2017 - 17:47

score 198 · Answer 10 · 2017-08-29 11:03:30

198

Views

Standard topology exercise

Published on 29 Aug 2017 - 11:03

score 142 · Answer 11 · 2017-08-29 22:14:16

142

Views

Standard topology exercise with interior, compactness,connectedness

Published on 29 Aug 2017 - 22:14

score 253 · Answer 12 · 2017-08-30 12:23:15

253

Views

Exercise about the topology $\tau=\{A\subset\mathbb{R}; (\forall x \in A \cap \mathbb{Z})(\exists\epsilon>0): (x-\epsilon,x+\epsilon) \subset A\}$

Published on 30 Aug 2017 - 12:23

score 41 · Answer 13 · 2026-02-23 20:57:48

41

Views

Are all topologies that are generated by uniform spaces $T_1$?

Published on 23 Feb 2026 - 20:57

score 118 · Answer 14 · 2017-09-01 16:57:04

118

Views

Why the separation axiom $T_0$ isn't implied by the others?

Published on 01 Sep 2017 - 16:57

score 661 · Answer 15 · 2017-09-06 00:40:44

661

Views

$X$ is normal if and only if $A\subseteq U$ implies there exists $V$ such that $A\subseteq V\subseteq\overline{V}\subseteq U$

Published on 06 Sep 2017 - 0:40

List Question

The Hausdorff property versus closedness of the diagonal in the context of convergence spaces

$X$ compact Hausdorff space whose diagonal is a zero set: prove that the diagonal in $X \times X$ is a $G_{\delta}$ -set

Epimorphisms in the category of separated schemes

Prove that a countably compact, first countable $T_{2}$ space is regular.

A continuous open image of completely regular space need not be completely regular

Showing that if $x$ is a limit point of $A$ in a $T_1$ space, then every neighborhoood of $x$ contains infinitely many points of $A$?

Literature references for the evident 'arc'-version of 'paths in a space compose'.

Pre-image of Hausdorff space is Hausdorff

Does an homeomorphism preserve $T_1$?

Standard topology exercise

Standard topology exercise with interior, compactness,connectedness

Exercise about the topology $\tau=\{A\subset\mathbb{R}; (\forall x \in A \cap \mathbb{Z})(\exists\epsilon>0): (x-\epsilon,x+\epsilon) \subset A\}$

Are all topologies that are generated by uniform spaces $T_1$?

Why the separation axiom $T_0$ isn't implied by the others?

$X$ is normal if and only if $A\subseteq U$ implies there exists $V$ such that $A\subseteq V\subseteq\overline{V}\subseteq U$

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