List questions from second-countable

Published on 22 Mar 2026 - 20:39

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The continuous image of a First Countable Space need not be First Countable (Willard 16.B.1)

Published on 25 Mar 2026 - 2:50

540

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Is it true that the cardinality of the topology generated by a countable basis has at most cardinality $|P(\mathbb{N})|$?

Published on 19 Sep 2018 - 12:33

45

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Separable $\Rightarrow$ Lindelöf for metric spaces without using second-countability

Published on 05 Nov 2018 - 22:54

202

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Similarity and Difference between Separable Space and Separated space?

Published on 25 Mar 2026 - 3:18

99

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In a locally compact 2nd-countable Hausdorff space $E$ there is a sequence of compact subsets $K_n$ with $K_{n-1}⊆\overset∘{K_n}$ and $\bigcup_nK_n=E$

Published on 13 May 2019 - 15:38

215

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Adjunction spaces of second countable, locally compact, Hausdorff spaces

Published on 24 May 2019 - 4:41

1.8k

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Are countable topological spaces second-countable?

Published on 24 Jun 2019 - 10:45

385

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$L^{p}$ is separable for second countable space

Published on 26 Jun 2019 - 15:00

307

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Proving that $\Bbb Q^n$ is dense in $\Bbb R^n$

Published on 04 Aug 2019 - 2:19

165

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Proving that $\Bbb Q$ is dense in $\Bbb R$

Published on 04 Aug 2019 - 2:46

3.6k

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$\mathbb{R}^n$ Second Countable

Published on 05 Aug 2019 - 18:22

359

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0-manifolds are countable and discrete

Published on 09 Aug 2019 - 21:26

189

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Second countable space question

Published on 20 Mar 2014 - 12:07

2k

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Compact topological space not having Countable Basis?

Published on 10 Apr 2014 - 23:03

List Question

Uncountable product of second countable spaces

The continuous image of a First Countable Space need not be First Countable (Willard 16.B.1)

Is it true that the cardinality of the topology generated by a countable basis has at most cardinality $|P(\mathbb{N})|$?

Separable $\Rightarrow$ Lindelöf for metric spaces without using second-countability

Similarity and Difference between Separable Space and Separated space?

In a locally compact 2nd-countable Hausdorff space $E$ there is a sequence of compact subsets $K_n$ with $K_{n-1}⊆\overset∘{K_n}$ and $\bigcup_nK_n=E$

Adjunction spaces of second countable, locally compact, Hausdorff spaces

Are countable topological spaces second-countable?

$L^{p}$ is separable for second countable space

Proving that $\Bbb Q^n$ is dense in $\Bbb R^n$

Proving that $\Bbb Q$ is dense in $\Bbb R$

$\mathbb{R}^n$ Second Countable

0-manifolds are countable and discrete

Second countable space question

Compact topological space not having Countable Basis?

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