List questions from second-countable

Published on 23 Feb 2026 - 5:13

63

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

Published on 13 Mar 2024 - 17:56

5.5k

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

Published on 20 Jan 2015 - 4:19

1.4k

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

Published on 03 Feb 2015 - 23:04

10.2k

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Second Countable, First Countable, and Separable Spaces

Published on 16 Mar 2015 - 5:06

191

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

Published on 03 Jun 2015 - 16:16

3k

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Is a separable and metrizable space second countable?

Published on 10 Sep 2015 - 21:45

2.9k

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First countable + separable imply second countable?

Published on 21 Jan 2016 - 3:27

6.6k

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Show that every compact metrizable space has a countable basis

Published on 06 Feb 2016 - 5:51

177

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

Published on 06 Feb 2016 - 7:19

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 22 Mar 2026 - 10:48

2.4k

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Is one-point compactification of a space metrizable

Published on 10 Feb 2016 - 17:18

160

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Prove topological space has countable basis

Published on 22 Mar 2016 - 0:46

7k

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Every separable metric space has a countable base

Published on 03 Jun 2016 - 4:59

1.4k

Views

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

Published on 12 Jun 2016 - 17:34

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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