Question

Extremally disconnected implies $T_1$?

score 120 · Answer 1 · 2026-04-14 20:56:33

120

Views

Extremally disconnected implies $T_1$?

Published on 14 Apr 2026 - 20:56

score 60 · Answer 2 · 2026-04-15 07:46:28

60

Views

Consider $\mathbb{R}^3/E$ with $E = \{(x,y,z) \in \mathbb{R}^2 \vert x^2 + y^2 + z^2 \leq 1\}$

Published on 15 Apr 2026 - 7:46

score 1k · Answer 3 · 2026-04-15 12:56:14

1k

Views

A topological space is regular if and only if for each $x \in X$ there exist a local base of closed neighbourhoods.

Published on 15 Apr 2026 - 12:56

score 816 · Answer 4 · 2026-04-15 23:26:46

816

Views

Image under covering map of Hausdorff space is Hausdorff?

Published on 15 Apr 2026 - 23:26

score 246 · Answer 5 · 2026-04-16 11:00:34

246

Views

Is the product of a $T_4$ space and a compact $T_4$ space necessarily $T_4$?

Published on 16 Apr 2026 - 11:00

score 468 · Answer 6 · 2026-04-10 23:32:04

468

Views

The product of perfectly normal compact Hausdorff spaces is perfectly normal

Published on 10 Apr 2026 - 23:32

score 10.8k · Answer 7 · 2026-04-11 14:27:34

10.8k

Views

Proof that every metric space is normal

Published on 11 Apr 2026 - 14:27

score 83 · Answer 8 · 2026-04-16 13:23:11

83

Views

Proving a Tychonoff Space $(T_{3.5})$ is finitely productive

Published on 16 Apr 2026 - 13:23

score 346 · Answer 9 · 2026-04-15 10:54:43

346

Views

If a topological space is regular-$G_\delta$, is it normal?

Published on 15 Apr 2026 - 10:54

score 918 · Answer 10 · 2026-04-16 11:10:11

918

Views

Proving a topological space is Tychonoff (completely regular) iff it has a base of cozero sets.

Published on 16 Apr 2026 - 11:10

score 79 · Answer 11 · 2026-04-15 16:08:35

79

Views

On proving that if $\prod_{\alpha \in \Lambda}X_\alpha$ is $T_i$ with $i \in \{3,4\}$ then $X_\alpha$ is $T_i$ for all $\alpha$.

Published on 15 Apr 2026 - 16:08

score 312 · Answer 12 · 2026-04-11 20:41:23

312

Views

Finite Complement Topology, Compactness, and Closedness

Published on 11 Apr 2026 - 20:41

score 110 · Answer 13 · 2026-04-13 17:01:22

110

Views

Is $\tau=\{\mathbb{R},\emptyset$ and every interval $(-n,n)\}$ a $T_1$ -space

Published on 13 Apr 2026 - 17:01

score 394 · Answer 14 · 2026-04-17 14:54:24

394

Views

Subcategories of T1, Hausdorff and TD spaces are reflective subcategories of Category Top.

Published on 17 Apr 2026 - 14:54

score 821 · Answer 15 · 2026-04-15 10:57:49

821

Views

Show that this topology on the sphere is Hausdorff

Published on 15 Apr 2026 - 10:57

List Question

Extremally disconnected implies $T_1$?

Consider $\mathbb{R}^3/E$ with $E = \{(x,y,z) \in \mathbb{R}^2 \vert x^2 + y^2 + z^2 \leq 1\}$

A topological space is regular if and only if for each $x \in X$ there exist a local base of closed neighbourhoods.

Image under covering map of Hausdorff space is Hausdorff?

Is the product of a $T_4$ space and a compact $T_4$ space necessarily $T_4$?

The product of perfectly normal compact Hausdorff spaces is perfectly normal

Proof that every metric space is normal

Proving a Tychonoff Space $(T_{3.5})$ is finitely productive

If a topological space is regular-$G_\delta$, is it normal?

Proving a topological space is Tychonoff (completely regular) iff it has a base of cozero sets.

On proving that if $\prod_{\alpha \in \Lambda}X_\alpha$ is $T_i$ with $i \in \{3,4\}$ then $X_\alpha$ is $T_i$ for all $\alpha$.

Finite Complement Topology, Compactness, and Closedness

Is $\tau=\{\mathbb{R},\emptyset$ and every interval $(-n,n)\}$ a $T_1$ -space

Subcategories of T1, Hausdorff and TD spaces are reflective subcategories of Category Top.

Show that this topology on the sphere is Hausdorff

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