Question

$X$ compact Hausdorff space whose diagonal is a zero set: prove that the diagonal in $X \times X$ is a $G_{\delta}$ -set

score 248 · Answer 1 · 2017-07-31 01:01:03

248

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$X$ compact Hausdorff space whose diagonal is a zero set: prove that the diagonal in $X \times X$ is a $G_{\delta}$ -set

Published on 31 Jul 2017 - 1:01

score 394 · Answer 2 · 2017-09-21 00:33:32

394

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Separable, metrizable, and second countable spaces

Published on 21 Sep 2017 - 0:33

score 64 · Answer 3 · 2026-02-23 01:05:16

64

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Prove that $\mathbb R_l$ $\times$ $\mathbb R_l$ given the box topology has a countable dense subset.

Published on 23 Feb 2026 - 1:05

score 274 · Answer 4 · 2017-09-29 16:15:51

274

Views

Give a subspace of $\mathbb R_l \times \mathbb R_l$ that has no countable dense subset [relative to the subspace topology].

Published on 29 Sep 2017 - 16:15

score 745 · Answer 5 · 2017-11-02 06:11:24

745

Views

Indiscrete topological space is second countable.

Published on 02 Nov 2017 - 6:11

score 1.2k · Answer 6 · 2017-11-26 23:30:29

1.2k

Views

Determine if $\mathbb{R}^{\omega}$ with the product topology is second countable

Published on 26 Nov 2017 - 23:30

score 1.7k · Answer 7 · 2017-11-26 23:44:29

1.7k

Views

Prove that $\mathbb{R}_l$ is not a second countable. ($\mathbb{R}_l$ are the real ones with the topology of the lower limit)

Published on 26 Nov 2017 - 23:44

score 107 · Answer 8 · 2017-12-07 13:16:38

107

Views

How does the underlying topological space of manifold depend on the properties of the atlas?

Published on 07 Dec 2017 - 13:16

score 175 · Answer 9 · 2017-12-29 20:50:21

175

Views

$X^$ with $w^$-topology second countable for separable Banach space $X$?

Published on 29 Dec 2017 - 20:50

score 1.4k · Answer 10 · 2011-03-08 22:50:04

1.4k

Views

Does there exist a Connected Locally Euclidean Space that is not second countable?

Published on 08 Mar 2011 - 22:50

score 4.5k · Answer 11 · 2011-08-14 03:41:33

4.5k

Views

Hausdorff locally compact and second countable is $\sigma$-compact

Published on 14 Aug 2011 - 3:41

score 352 · Answer 12 · 2011-09-28 23:30:20

352

Views

In this proof that a compact metric space is second countable, why exactly is the induced topology the same as the metric topology?

Published on 28 Sep 2011 - 23:30

score 1.8k · Answer 13 · 2011-12-10 17:07:54

1.8k

Views

Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?

Published on 10 Dec 2011 - 17:07

score 2.3k · Answer 14 · 2012-05-15 02:06:24

2.3k

Views

Equivalence of three properties of a metric space.

Published on 15 May 2012 - 2:06

score 735 · Answer 15 · 2012-07-23 01:06:30

735

Views

Being second countable is invariant under perfect mapping

Published on 23 Jul 2012 - 1:06

List Question

$X$ compact Hausdorff space whose diagonal is a zero set: prove that the diagonal in $X \times X$ is a $G_{\delta}$ -set

Separable, metrizable, and second countable spaces

Prove that $\mathbb R_l$ $\times$ $\mathbb R_l$ given the box topology has a countable dense subset.

Give a subspace of $\mathbb R_l \times \mathbb R_l$ that has no countable dense subset [relative to the subspace topology].

Indiscrete topological space is second countable.

Determine if $\mathbb{R}^{\omega}$ with the product topology is second countable

Prove that $\mathbb{R}_l$ is not a second countable. ($\mathbb{R}_l$ are the real ones with the topology of the lower limit)

How does the underlying topological space of manifold depend on the properties of the atlas?

$X^$ with $w^$-topology second countable for separable Banach space $X$?

Does there exist a Connected Locally Euclidean Space that is not second countable?

Hausdorff locally compact and second countable is $\sigma$-compact

In this proof that a compact metric space is second countable, why exactly is the induced topology the same as the metric topology?

Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?

Equivalence of three properties of a metric space.

Being second countable is invariant under perfect mapping

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