Question

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

score 144 · Answer 1 · 2026-04-13 05:28:10

144

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

Published on 13 Apr 2026 - 5:28

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 57 · Answer 3 · 2026-05-11 00:37:05

57

Views

Box topology first countability

Published on 11 May 2026 - 0:37

score 203 · Answer 4 · 2026-04-14 03:10:34

203

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 Apr 2026 - 3:10

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 990 · Answer 6 · 2026-04-12 23:10:10

990

Views

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

Published on 12 Apr 2026 - 23:10

score 119 · Answer 7 · 2026-04-11 11:05:19

119

Views

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

Published on 11 Apr 2026 - 11:05

score 44 · Answer 8 · 2026-04-10 10:57:45

44

Views

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

Published on 10 Apr 2026 - 10:57

score 73 · Answer 9 · 2026-04-11 14:38:34

73

Views

Interior of a set and first countability

Published on 11 Apr 2026 - 14:38

score 118 · Answer 10 · 2026-04-09 16:09:09

118

Views

When is an absolute Galois group first-countable?

Published on 09 Apr 2026 - 16:09

score 93 · Answer 11 · 2026-04-13 19:36:15

93

Views

Countable set if the cardinal number is smaller than aleph null

Published on 13 Apr 2026 - 19:36

score 222 · Answer 12 · 2026-04-10 05:15:45

222

Views

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

Published on 10 Apr 2026 - 5:15

score 146 · Answer 13 · 2026-04-12 03:04:43

146

Views

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

Published on 12 Apr 2026 - 3:04

score 48 · Answer 14 · 2026-04-10 23:00:23

48

Views

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

Published on 10 Apr 2026 - 23:00

score 435 · Answer 15 · 2026-04-14 14:45:07

435

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 14 Apr 2026 - 14:45

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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