Question

Proving $B(A)$ is countable.

score 81 · Answer 1 · 2026-04-10 20:32:46

81

Views

Proving $B(A)$ is countable.

Published on 10 Apr 2026 - 20:32

score 203 · Answer 2 · 2026-03-25 11:14:54

203

Views

Are the set of all convergent geometric series whose sum is a rational number is countable?

Published on 25 Mar 2026 - 11:14

score 223 · Answer 3 · 2026-03-25 12:50:47

223

Views

If $X$ and $Y$ are first countable then $\lim_{x\to x_0}f(x)=y_0$ iff $\lim_{n\to+\infty}f(x_n)=y_0$ for any $x_n\to x_0$

Published on 25 Mar 2026 - 12:50

score 49 · Answer 4 · 2026-03-25 12:49:48

49

Views

If $f:X\rightarrow Y$ is not a constant function and if $X$ is first countable then $f$ is not continuous in any isolated point of $X$.

Published on 25 Mar 2026 - 12:49

score 175 · Answer 5 · 2026-03-25 14:22:32

175

Views

First countable property for $\operatorname{spec}(\mathbb{C}[x])$ with Zariski topology

Published on 25 Mar 2026 - 14:22

score 87 · Answer 6 · 2026-04-13 04:04:50

87

Views

The family of non-decreasing functions from the segment info itself endowed with the topology of pointwise convergence is first countable

Published on 13 Apr 2026 - 4:04

score 284 · Answer 7 · 2026-04-15 01:39:02

284

Views

Constraining a dense sequence on a product space, one factor at a time

Published on 15 Apr 2026 - 1:39

score 194 · Answer 8 · 2026-04-12 20:53:47

194

Views

If every point of a compact Hausdorff space is the intersection of a nested sequence of open sets then is the space first-countable?

Published on 12 Apr 2026 - 20:53

score 128 · Answer 9 · 2026-04-11 17:57:53

128

Views

Checking for countinuity and countability axioms for this topology on the real plane $\mathbb{R}^2$

Published on 11 Apr 2026 - 17:57

score 919 · Answer 10 · 2026-04-15 13:11:51

919

Views

A first countable Hausdorff space is compactly generated

Published on 15 Apr 2026 - 13:11

score 315 · Answer 11 · 2026-05-10 17:56:06

315

Views

Some question about first (or second) countable - first (second) "countabilization"

Published on 10 May 2026 - 17:56

score 826 · Answer 12 · 2026-04-08 21:22:42

826

Views

To prove $\omega_1 \cup \{\omega_1\} $ is not first countable but $\omega_1$ is

Published on 08 Apr 2026 - 21:22

score 44 · Answer 13 · 2026-04-14 09:19:45

44

Views

Existance of a countable base for $\mathbb R$

Published on 14 Apr 2026 - 9:19

score 61 · Answer 14 · 2026-05-10 19:50:26

61

Views

Are first and second countability preserved under intersection of topologies?

Published on 10 May 2026 - 19:50

score 104 · Answer 15 · 2026-04-11 12:14:07

104

Views

Topology question on first countable.

Published on 11 Apr 2026 - 12:14

List Question

Proving $B(A)$ is countable.

Are the set of all convergent geometric series whose sum is a rational number is countable?

If $X$ and $Y$ are first countable then $\lim_{x\to x_0}f(x)=y_0$ iff $\lim_{n\to+\infty}f(x_n)=y_0$ for any $x_n\to x_0$

If $f:X\rightarrow Y$ is not a constant function and if $X$ is first countable then $f$ is not continuous in any isolated point of $X$.

First countable property for $\operatorname{spec}(\mathbb{C}[x])$ with Zariski topology

The family of non-decreasing functions from the segment info itself endowed with the topology of pointwise convergence is first countable

Constraining a dense sequence on a product space, one factor at a time

If every point of a compact Hausdorff space is the intersection of a nested sequence of open sets then is the space first-countable?

Checking for countinuity and countability axioms for this topology on the real plane $\mathbb{R}^2$

A first countable Hausdorff space is compactly generated

Some question about first (or second) countable - first (second) "countabilization"

To prove $\omega_1 \cup \{\omega_1\} $ is not first countable but $\omega_1$ is

Existance of a countable base for $\mathbb R$

Are first and second countability preserved under intersection of topologies?

Topology question on first countable.

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