Question

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

score 139 · Answer 1 · 2026-04-15 06:18:59

139

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 15 Apr 2026 - 6:18

score 351 · Answer 2 · 2026-03-25 14:00:39

351

Views

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

Published on 25 Mar 2026 - 14:00

score 628 · Answer 3 · 2026-03-25 13:51:05

628

Views

Every compact metrizable space is second countable

Published on 25 Mar 2026 - 13:51

score 555 · Answer 4 · 2026-03-25 13:54:43

555

Views

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

Published on 25 Mar 2026 - 13:54

score 982 · Answer 5 · 2026-05-01 14:46:14

982

Views

Every Riemann Surface has a countable basis for its topology

Published on 01 May 2026 - 14:46

score 284 · Answer 6 · 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 1.1k · Answer 7 · 2026-04-15 11:25:11

1.1k

Views

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

Published on 15 Apr 2026 - 11:25

score 145 · Answer 8 · 2026-04-10 21:05:56

145

Views

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

Published on 10 Apr 2026 - 21:05

score 376 · Answer 9 · 2026-04-13 23:01:51

376

Views

Does every compact metric space have a finite basis?

Published on 13 Apr 2026 - 23:01

score 314 · Answer 10 · 2026-04-11 04:38:04

314

Views

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

Published on 11 Apr 2026 - 4:38

score 79 · Answer 11 · 2026-04-17 06:46:19

79

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 17 Apr 2026 - 6:46

score 188 · Answer 12 · 2026-04-11 12:36:23

188

Views

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

Published on 11 Apr 2026 - 12:36

score 145 · Answer 13 · 2026-04-15 03:57:57

145

Views

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

Published on 15 Apr 2026 - 3:57

score 825 · Answer 14 · 2026-04-10 17:14:08

825

Views

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

Published on 10 Apr 2026 - 17:14

score 131 · Answer 15 · 2026-04-15 18:25:55

131

Views

second-countability of the upper halfplane

Published on 15 Apr 2026 - 18:25

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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