Question

Is every completely regular topology induced by some proximity?

score 40 · Answer 1 · 2019-02-12 15:35:13

40

Views

Is every completely regular topology induced by some proximity?

Published on 12 Feb 2019 - 15:35

score 68 · Answer 2 · 2019-02-12 16:38:14

68

Views

Another equivalent condition for being $T_1$−space $(X,\mathscr T)$ is normal.

Published on 12 Feb 2019 - 16:38

score 56 · Answer 3 · 2019-02-14 23:37:46

56

Views

What separation axiom is necessary for existence of neighborhood which closure is a subset of another given neighborhood

Published on 14 Feb 2019 - 23:37

score 90 · Answer 4 · 2019-02-19 01:51:37

90

Views

Is every completely regular topology induced by some topological vector space?

Published on 19 Feb 2019 - 1:51

score 65 · Answer 5 · 2019-02-22 17:35:35

65

Views

$X$ $T_3$ and $f:X\rightarrow Y$ cont. open and closed $\Longrightarrow$ $f(X)$ Hausdorff

Published on 22 Feb 2019 - 17:35

score 36 · Answer 6 · 2019-03-02 06:19:07

36

Views

Can we prove the theorem without injectivity of $f$?

Published on 02 Mar 2019 - 6:19

score 309 · Answer 7 · 2019-03-06 23:59:10

309

Views

Bourbaki General Topology I: Exercise 20, sec. 8 ch.1

Published on 06 Mar 2019 - 23:59

score 205 · Answer 8 · 2019-03-10 06:17:40

205

Views

Singletons closed in infinite T1 Product Topology?

Published on 10 Mar 2019 - 6:17

score 284 · Answer 9 · 2019-03-12 10:07:56

284

Views

Example of a locally compact + Hausdorff + ¬normal + connected space

Published on 12 Mar 2019 - 10:07

score 333 · Answer 10 · 2026-03-22 14:39:06

333

Views

Is $\mathbb R^J$ normal in the box topology when $J$ is uncountable?

Published on 22 Mar 2026 - 14:39

score 273 · Answer 11 · 2019-03-14 17:50:44

273

Views

On exercise 14H from Willard's 'General Topology' book

Published on 14 Mar 2019 - 17:50

score 576 · Answer 12 · 2019-03-20 00:07:14

576

Views

$(X,\mathscr T)$ is normal and each closed subsets of $X$ is a $G_{\delta}$ set.Then, $(X,\mathscr T)$ perfectly normal.

Published on 20 Mar 2019 - 0:07

score 247 · Answer 13 · 2019-03-29 14:54:07

247

Views

Showing $\mathbb{N}$ with the topology generated from arithmetic progression is $T_2$ but not $T_3$

Published on 29 Mar 2019 - 14:54

score 273 · Answer 14 · 2019-03-30 21:29:13

273

Views

Equivalence of $T_1$ axiom definition

Published on 30 Mar 2019 - 21:29

score 896 · Answer 15 · 2019-03-30 23:40:16

896

Views

Inverse image of singleton sets under continuous map between compact Hausdorff topological spaces

Published on 30 Mar 2019 - 23:40

List Question

Is every completely regular topology induced by some proximity?

Another equivalent condition for being $T_1$−space $(X,\mathscr T)$ is normal.

What separation axiom is necessary for existence of neighborhood which closure is a subset of another given neighborhood

Is every completely regular topology induced by some topological vector space?

$X$ $T_3$ and $f:X\rightarrow Y$ cont. open and closed $\Longrightarrow$ $f(X)$ Hausdorff

Can we prove the theorem without injectivity of $f$?

Bourbaki General Topology I: Exercise 20, sec. 8 ch.1

Singletons closed in infinite T1 Product Topology?

Example of a locally compact + Hausdorff + ¬normal + connected space

Is $\mathbb R^J$ normal in the box topology when $J$ is uncountable?

On exercise 14H from Willard's 'General Topology' book

$(X,\mathscr T)$ is normal and each closed subsets of $X$ is a $G_{\delta}$ set.Then, $(X,\mathscr T)$ perfectly normal.

Showing $\mathbb{N}$ with the topology generated from arithmetic progression is $T_2$ but not $T_3$

Equivalence of $T_1$ axiom definition

Inverse image of singleton sets under continuous map between compact Hausdorff topological spaces

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