Question

$X-\bigcup \lbrace A_{n}: n \in \mathbb{N} \rbrace$ dense in $X$ if $X$ compact Haussdorff and $A_{n}$ nowherdense in $X$ for each $n \in \mathbb{N}$

score 60 · Answer 1 · 2021-05-21 19:27:53

60

Views

$X-\bigcup \lbrace A_{n}: n \in \mathbb{N} \rbrace$ dense in $X$ if $X$ compact Haussdorff and $A_{n}$ nowherdense in $X$ for each $n \in \mathbb{N}$

Published on 21 May 2021 - 19:27

score 46 · Answer 2 · 2021-05-22 20:43:26

46

Views

Locally Finite Alexandroff Space not T1 over continuous function

Published on 22 May 2021 - 20:43

score 249 · Answer 3 · 2021-05-23 17:52:55

249

Views

Munkres' Topology, 2nd edition, Theorem 34.3 at page 218, confusion.

Published on 23 May 2021 - 17:52

score 839 · Answer 4 · 2021-06-02 21:47:06

839

Views

Prove $X$ is Hausdorff if and only if $Y$ is Hausdorff

Published on 02 Jun 2021 - 21:47

score 176 · Answer 5 · 2021-06-03 01:50:04

176

Views

Confusion about regular and $T_1$ spaces

Published on 03 Jun 2021 - 1:50

score 181 · Answer 6 · 2021-06-06 14:11:47

181

Views

Space is $T_1$ iff finite subsets are closed: alternative approach

Published on 06 Jun 2021 - 14:11

score 89 · Answer 7 · 2021-06-07 21:34:56

89

Views

T1 space, there all closed G-delta set is zero-set, but isn't normal

Published on 07 Jun 2021 - 21:34

score 155 · Answer 8 · 2021-06-08 16:21:05

155

Views

Collection of all compact subsets of a Hausdorff space $X$ is compact if and only if $X$ is compact.

Published on 08 Jun 2021 - 16:21

score 93 · Answer 9 · 2021-06-10 09:40:22

How do I show that if $A$ is compact and $U \supseteq A$ is open, then there is an open $V$ with $A \subseteq V \subseteq \overline{V} \subseteq U$?

score 193 · Answer 10 · 2021-06-10 11:03:37

193

Views

Proving completely regular is a topological property

Published on 10 Jun 2021 - 11:03

score 306 · Answer 11 · 2021-06-11 13:57:01

306

Views

A $T_1$ - space is normal if and only if...

Published on 11 Jun 2021 - 13:57

score 75 · Answer 12 · 2021-06-14 14:02:47

75

Views

why $U_{y_1}\cap ....\cap U_{y_n}$? why not $U_{y_1}\cup ....\cup U_{y_n}?$

Published on 14 Jun 2021 - 14:02

score 77 · Answer 13 · 2021-06-21 20:43:28

77

Views

Is $(\mathbb{R}, \tau)$ normal, irrespective of the nature of $\tau$?

Published on 21 Jun 2021 - 20:43

score 149 · Answer 14 · 2021-06-22 03:02:26

149

Views

Non T1 space with every convergent sequence is eventually constant

Published on 22 Jun 2021 - 3:02

score 39 · Answer 15 · 2021-06-22 20:58:36

39

Views

Necessity and sufficient condition of perfectly normality

Published on 22 Jun 2021 - 20:58

List Question

$X-\bigcup \lbrace A_{n}: n \in \mathbb{N} \rbrace$ dense in $X$ if $X$ compact Haussdorff and $A_{n}$ nowherdense in $X$ for each $n \in \mathbb{N}$

Locally Finite Alexandroff Space not T1 over continuous function

Munkres' Topology, 2nd edition, Theorem 34.3 at page 218, confusion.

Prove $X$ is Hausdorff if and only if $Y$ is Hausdorff

Confusion about regular and $T_1$ spaces

Space is $T_1$ iff finite subsets are closed: alternative approach

T1 space, there all closed G-delta set is zero-set, but isn't normal

Collection of all compact subsets of a Hausdorff space $X$ is compact if and only if $X$ is compact.

How do I show that if $A$ is compact and $U \supseteq A$ is open, then there is an open $V$ with $A \subseteq V \subseteq \overline{V} \subseteq U$?

Proving completely regular is a topological property

A $T_1$ - space is normal if and only if...

why $U_{y_1}\cap ....\cap U_{y_n}$? why not $U_{y_1}\cup ....\cup U_{y_n}?$

Is $(\mathbb{R}, \tau)$ normal, irrespective of the nature of $\tau$?

Non T1 space with every convergent sequence is eventually constant

Necessity and sufficient condition of perfectly normality

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