Question

Proving $B(A)$ is countable.

score 79 · Answer 1 · 2020-05-15 23:33:50

79

Views

Proving $B(A)$ is countable.

Published on 15 May 2020 - 23:33

score 202 · Answer 2 · 2020-05-28 19:11:10

202

Views

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

Published on 28 May 2020 - 19:11

score 222 · Answer 3 · 2020-06-29 21:19:07

222

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 29 Jun 2020 - 21:19

score 48 · Answer 4 · 2020-07-03 09:48:38

48

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 03 Jul 2020 - 9:48

score 174 · Answer 5 · 2020-07-11 21:22:22

174

Views

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

Published on 11 Jul 2020 - 21:22

score 84 · Answer 6 · 2016-08-19 03:45:01

84

Views

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

Published on 19 Aug 2016 - 3:45

score 281 · Answer 7 · 2016-09-04 06:00:21

281

Views

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

Published on 04 Sep 2016 - 6:00

score 191 · Answer 8 · 2016-09-05 12:53:17

191

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 05 Sep 2016 - 12:53

score 125 · Answer 9 · 2016-09-11 16:14:59

125

Views

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

Published on 11 Sep 2016 - 16:14

score 916 · Answer 10 · 2016-11-22 17:45:07

916

Views

A first countable Hausdorff space is compactly generated

Published on 22 Nov 2016 - 17:45

score 311 · Answer 11 · 2016-11-29 03:57:29

311

Views

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

Published on 29 Nov 2016 - 3:57

score 823 · Answer 12 · 2016-12-27 06:01:48

823

Views

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

Published on 27 Dec 2016 - 6:01

score 41 · Answer 13 · 2017-01-29 14:17:31

41

Views

Existance of a countable base for $\mathbb R$

Published on 29 Jan 2017 - 14:17

score 59 · Answer 14 · 2023-02-14 22:03:58

59

Views

Are first and second countability preserved under intersection of topologies?

Published on 14 Feb 2023 - 22:03

score 101 · Answer 15 · 2023-02-15 21:21:46

101

Views

Topology question on first countable.

Published on 15 Feb 2023 - 21:21

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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