Question

Extremally disconnected implies $T_1$?

score 117 · Answer 1 · 2018-06-14 16:18:00

117

Views

Extremally disconnected implies $T_1$?

Published on 14 Jun 2018 - 16:18

score 58 · Answer 2 · 2018-06-22 12:23:39

58

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 22 Jun 2018 - 12:23

score 1k · Answer 3 · 2018-06-28 10:26:29

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 28 Jun 2018 - 10:26

score 813 · Answer 4 · 2018-07-14 20:34:23

813

Views

Image under covering map of Hausdorff space is Hausdorff?

Published on 14 Jul 2018 - 20:34

score 243 · Answer 5 · 2018-07-21 21:34:51

243

Views

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

Published on 21 Jul 2018 - 21:34

score 465 · Answer 6 · 2018-08-04 15:27:39

465

Views

The product of perfectly normal compact Hausdorff spaces is perfectly normal

Published on 04 Aug 2018 - 15:27

score 10.8k · Answer 7 · 2018-08-04 21:29:16

10.8k

Views

Proof that every metric space is normal

Published on 04 Aug 2018 - 21:29

score 80 · Answer 8 · 2018-08-08 18:30:53

80

Views

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

Published on 08 Aug 2018 - 18:30

score 343 · Answer 9 · 2018-08-24 05:31:54

343

Views

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

Published on 24 Aug 2018 - 5:31

score 915 · Answer 10 · 2018-08-30 00:27:36

915

Views

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

Published on 30 Aug 2018 - 0:27

score 76 · Answer 11 · 2018-09-24 23:06:36

76

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 24 Sep 2018 - 23:06

score 309 · Answer 12 · 2018-09-27 14:20:28

309

Views

Finite Complement Topology, Compactness, and Closedness

Published on 27 Sep 2018 - 14:20

score 108 · Answer 13 · 2018-09-28 10:51:30

108

Views

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

Published on 28 Sep 2018 - 10:51

score 392 · Answer 14 · 2018-09-30 10:24:21

392

Views

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

Published on 30 Sep 2018 - 10:24

score 818 · Answer 15 · 2018-10-02 12:44:41

818

Views

Show that this topology on the sphere is Hausdorff

Published on 02 Oct 2018 - 12:44

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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