Question

Prob. 16 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The product space $\mathbb{R}^I$, where $I = [0, 1]$, is separable

score 136 · Answer 1 · 2020-05-03 15:49:05

136

Views

Prob. 16 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The product space $\mathbb{R}^I$, where $I = [0, 1]$, is separable

Published on 03 May 2020 - 15:49

score 350 · Answer 2 · 2020-05-18 00:16:03

350

Views

Okay... but what does "second-countable" actually mean?

Published on 18 May 2020 - 0:16

score 627 · Answer 3 · 2016-07-31 22:28:33

627

Views

Every compact metrizable space is second countable

Published on 31 Jul 2016 - 22:28

score 554 · Answer 4 · 2016-08-01 22:37:14

554

Views

How to show that $\omega_1$ is not secound countable?

Published on 01 Aug 2016 - 22:37

score 980 · Answer 5 · 2026-02-23 02:42:22

980

Views

Every Riemann Surface has a countable basis for its topology

Published on 23 Feb 2026 - 2:42

score 282 · Answer 6 · 2026-03-25 11:10:46

282

Views

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

Published on 25 Mar 2026 - 11:10

score 1.1k · Answer 7 · 2016-10-04 22:12:41

1.1k

Views

cardinality of the Borel $\sigma$-algebra of a second countable space

Published on 04 Oct 2016 - 22:12

score 142 · Answer 8 · 2016-10-16 18:27:36

142

Views

How can I prove 'separable' guarantees 'second countable'?

Published on 16 Oct 2016 - 18:27

score 373 · Answer 9 · 2016-11-16 19:43:40

373

Views

Does every compact metric space have a finite basis?

Published on 16 Nov 2016 - 19:43

score 312 · Answer 10 · 2026-03-25 11:08:02

312

Views

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

Published on 25 Mar 2026 - 11:08

score 77 · Answer 11 · 2016-12-04 18:14:41

77

Views

$X$ top space with countable basis $B = \{B_n\}_{n\in \mathbb{N}}$. Then exists countable subset $D\subseteq X$, $\overline{D} = X$

Published on 04 Dec 2016 - 18:14

score 185 · Answer 12 · 2016-12-21 16:14:23

185

Views

Does having a countable subbasis also satisfy the second axiom of countability?

Published on 21 Dec 2016 - 16:14

score 142 · Answer 13 · 2017-01-12 20:56:28

142

Views

If $(E,\tau)$ is a topological space $E_2$, then $(E,\tau)$ is Lindelöf and separable.

Published on 12 Jan 2017 - 20:56

score 823 · Answer 14 · 2026-03-25 11:01:43

823

Views

The image of a second-countable space by a closed continuous mapping with compact fibers is second-countable

Published on 25 Mar 2026 - 11:01

score 128 · Answer 15 · 2017-02-22 21:49:47

128

Views

second-countability of the upper halfplane

Published on 22 Feb 2017 - 21:49

List Question

Prob. 16 (a), Sec. 30, in Munkres' TOPOLOGY, 2nd ed: The product space $\mathbb{R}^I$, where $I = [0, 1]$, is separable

Okay... but what does "second-countable" actually mean?

Every compact metrizable space is second countable

How to show that $\omega_1$ is not secound countable?

Every Riemann Surface has a countable basis for its topology

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

cardinality of the Borel $\sigma$-algebra of a second countable space

How can I prove 'separable' guarantees 'second countable'?

Does every compact metric space have a finite basis?

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

$X$ top space with countable basis $B = \{B_n\}_{n\in \mathbb{N}}$. Then exists countable subset $D\subseteq X$, $\overline{D} = X$

Does having a countable subbasis also satisfy the second axiom of countability?

If $(E,\tau)$ is a topological space $E_2$, then $(E,\tau)$ is Lindelöf and separable.

The image of a second-countable space by a closed continuous mapping with compact fibers is second-countable

second-countability of the upper halfplane

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