List questions from second-countable

Published on 20 Aug 2012 - 20:19

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Compact metrizable space has a countable basis (Munkres Topology)

Published on 10 Nov 2012 - 6:19

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Every $T_3$ space with a countable basis is $T_4$.

Published on 31 Jan 2013 - 11:55

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Second-countable implies separable/Axiom countable choice

Published on 20 Feb 2013 - 18:06

344

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Second countability of compact open topology

Published on 20 Sep 2020 - 5:16

716

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Manifold has a countable cover by compact sets.

Published on 28 Sep 2020 - 2:09

126

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Second countable space implies numerable subbasis

Published on 13 Oct 2020 - 3:30

94

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Examples of topologies in which all open sets are countable union of base elements, but the topology itself doesn't have countable bases.

Published on 23 Feb 2026 - 10:21

59

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Is this topology separable, first countable, second countable?

Published on 09 Nov 2020 - 11:26

157

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Let X be a topological space. a) If X is Hausdorff and it has an countable base, so X is normal?

Published on 16 Nov 2020 - 21:47

36

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Second countable space $\implies [x_n\to a, f(x_n)\to L \implies \lim\limits_{x\to a}f(x)=L]$

Published on 01 Dec 2020 - 17:45

284

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Does second countable implies countably many components?

Published on 05 Jan 2021 - 4:47

88

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Counter example in topology

Published on 14 Jan 2021 - 18:14

398

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Is the countable union of second countable open subspaces second countable?

Published on 09 Feb 2021 - 9:11

91

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Help me visualize a Lindelöf space and a corresponding theorem

Published on 23 Feb 2026 - 6:56

List Question

When is $C_0(X)$ separable?

Compact metrizable space has a countable basis (Munkres Topology)

Every $T_3$ space with a countable basis is $T_4$.

Second-countable implies separable/Axiom countable choice

Second countability of compact open topology

Manifold has a countable cover by compact sets.

Second countable space implies numerable subbasis

Examples of topologies in which all open sets are countable union of base elements, but the topology itself doesn't have countable bases.

Is this topology separable, first countable, second countable?

Let X be a topological space. a) If X is Hausdorff and it has an countable base, so X is normal?

Second countable space $\implies [x_n\to a, f(x_n)\to L \implies \lim\limits_{x\to a}f(x)=L]$

Does second countable implies countably many components?

Counter example in topology

Is the countable union of second countable open subspaces second countable?

Help me visualize a Lindelöf space and a corresponding theorem

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