List questions from second-countable

Published on 13 Apr 2026 - 12:06

583

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

Published on 22 Apr 2026 - 17:51

541

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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 25 Mar 2026 - 6:24

46

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

Published on 25 Mar 2026 - 6:24

202

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Similarity and Difference between Separable Space and Separated space?

Published on 25 Mar 2026 - 3:18

100

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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 25 Mar 2026 - 6:22

216

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Adjunction spaces of second countable, locally compact, Hausdorff spaces

Published on 25 Mar 2026 - 6:19

1.8k

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Are countable topological spaces second-countable?

Published on 25 Mar 2026 - 6:17

386

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

Published on 25 Mar 2026 - 6:17

308

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

Published on 25 Mar 2026 - 6:19

166

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

Published on 25 Mar 2026 - 6:19

3.6k

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$\mathbb{R}^n$ Second Countable

Published on 10 Apr 2026 - 23:58

361

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0-manifolds are countable and discrete

Published on 27 Mar 2026 - 16:36

194

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Second countable space question

Published on 14 Apr 2026 - 21:17

2k

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Compact topological space not having Countable Basis?

Published on 12 Apr 2026 - 12:58

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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