Question

Let $X$ and $Y$ be topological spaces and $f: X \to Y$ a function....

score 141 · Answer 1 · 2020-11-12 14:41:56

141

Views

Let $X$ and $Y$ be topological spaces and $f: X \to Y$ a function....

Published on 12 Nov 2020 - 14:41

score 58 · Answer 2 · 2026-03-21 22:20:00

58

Views

Let $X = [0,1]$ and $\sim$ have the following equivalence relation over $X$: is the quotient first countable?

Published on 21 Mar 2026 - 22:20

score 51 · Answer 3 · 2026-02-23 02:52:24

51

Views

Box topology first countability

Published on 23 Feb 2026 - 2:52

score 200 · Answer 4 · 2020-11-14 22:49:04

200

Views

Let $X$ be the disjoint union of copies of a subspace of $\mathbb{R}$. Is the quotient of $X$ by identifying accumulation points first countable?

Published on 14 Nov 2020 - 22:49

score 158 · Answer 5 · 2026-03-25 21:49:43

158

Views

Let X be a topological space. a) If X is Hausdorff and it has an countable base, so X is normal?

Published on 25 Mar 2026 - 21:49

score 987 · Answer 6 · 2020-11-20 15:17:00

987

Views

Show that $X :=$ {$0, 1$}$^{\mathbb R}$ is not first-countable.

Published on 20 Nov 2020 - 15:17

score 116 · Answer 7 · 2020-11-20 22:55:53

116

Views

Show that $Y$ is not first-countable at $[0]$

Published on 20 Nov 2020 - 22:55

score 41 · Answer 8 · 2020-12-18 13:27:42

41

Views

Help needed in understanding an argument in Theorem 2.47 of topology by Wayne Patty

Published on 18 Dec 2020 - 13:27

score 70 · Answer 9 · 2021-01-05 05:11:50

70

Views

Interior of a set and first countability

Published on 05 Jan 2021 - 5:11

score 115 · Answer 10 · 2021-01-14 13:27:48

115

Views

When is an absolute Galois group first-countable?

Published on 14 Jan 2021 - 13:27

score 90 · Answer 11 · 2021-01-18 19:30:50

90

Views

Countable set if the cardinal number is smaller than aleph null

Published on 18 Jan 2021 - 19:30

score 219 · Answer 12 · 2021-02-02 16:31:48

219

Views

First countable compact spaces are sequentially compact, how weaker assumption ease the proof?

Published on 02 Feb 2021 - 16:31

score 143 · Answer 13 · 2026-02-23 04:52:10

143

Views

First countability of $[0,1]^\mathbb{R}$

Published on 23 Feb 2026 - 4:52

score 45 · Answer 14 · 2021-04-09 11:49:03

45

Views

Is there a topology on natural numbers being not first countable?

Published on 09 Apr 2021 - 11:49

score 432 · Answer 15 · 2021-04-19 14:06:10

432

Views

Verifying proof that in a first countable space if $x_n\to x$ and $f(x_n)\to f(x)$, then $f$ is continuous

Published on 19 Apr 2021 - 14:06

List Question

Let $X$ and $Y$ be topological spaces and $f: X \to Y$ a function....

Let $X = [0,1]$ and $\sim$ have the following equivalence relation over $X$: is the quotient first countable?

Box topology first countability

Let $X$ be the disjoint union of copies of a subspace of $\mathbb{R}$. Is the quotient of $X$ by identifying accumulation points first countable?

Let X be a topological space. a) If X is Hausdorff and it has an countable base, so X is normal?

Show that $X :=$ {$0, 1$}$^{\mathbb R}$ is not first-countable.

Show that $Y$ is not first-countable at $[0]$

Help needed in understanding an argument in Theorem 2.47 of topology by Wayne Patty

Interior of a set and first countability

When is an absolute Galois group first-countable?

Countable set if the cardinal number is smaller than aleph null

First countable compact spaces are sequentially compact, how weaker assumption ease the proof?

First countability of $[0,1]^\mathbb{R}$

Is there a topology on natural numbers being not first countable?

Verifying proof that in a first countable space if $x_n\to x$ and $f(x_n)\to f(x)$, then $f$ is continuous

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