List questions from second-countable

Published on 02 May 2026 - 19:08

64

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Proof about a property of $\mathbb{R}$

Published on 25 Mar 2026 - 17:19

5.5k

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When is the quotient space of a second countable space second countable?

Published on 25 Mar 2026 - 17:26

1.4k

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Why must a locally compact second countable Hausdorff space be second countable to imply paracompactness?

Published on 25 Mar 2026 - 17:24

10.2k

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Second Countable, First Countable, and Separable Spaces

Published on 25 Mar 2026 - 15:56

192

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Are the names such as $N_1$-space, $N_2$-space used for various countability axioms?

Published on 25 Mar 2026 - 16:03

3k

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Is a separable and metrizable space second countable?

Published on 25 Mar 2026 - 17:26

2.9k

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First countable + separable imply second countable?

Published on 28 Apr 2026 - 21:37

6.6k

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Show that every compact metrizable space has a countable basis

Published on 23 Apr 2026 - 9:34

179

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Munkres Topology Article -30 Problem 5: metrizable space with a countable dense set has a countable basis

Published on 04 May 2026 - 19:37

1.2k

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The space of continuous functions on an interval has a countable dense subset and a countable basis

Published on 21 Apr 2026 - 14:33

2.4k

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Is one-point compactification of a space metrizable

Published on 26 Mar 2026 - 19:41

161

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Prove topological space has countable basis

Published on 25 Mar 2026 - 17:23

7k

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Every separable metric space has a countable base

Published on 15 Apr 2026 - 20:37

1.4k

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If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis

Published on 18 Apr 2026 - 4:31

List Question

Is a $\sigma$-locally finite collection of open sets locally countable?

Proof about a property of $\mathbb{R}$

When is the quotient space of a second countable space second countable?

Why must a locally compact second countable Hausdorff space be second countable to imply paracompactness?

Second Countable, First Countable, and Separable Spaces

Are the names such as $N_1$-space, $N_2$-space used for various countability axioms?

Is a separable and metrizable space second countable?

First countable + separable imply second countable?

Show that every compact metrizable space has a countable basis

Munkres Topology Article -30 Problem 5: metrizable space with a countable dense set has a countable basis

The space of continuous functions on an interval has a countable dense subset and a countable basis

Is one-point compactification of a space metrizable

Prove topological space has countable basis

Every separable metric space has a countable base

If $(X, \mathcal{T})$ has a countable subbasis, then it has a countable basis

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