List questions from separation-axioms

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Proving that a compact subset of a Hausdorff space is closed

Published on 18 Jun 2015 - 4:39

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Compact Hausdorff spaces are normal

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existence of functionals

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Is the Alexandroff double circle compact and Hausdorff?

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Hausdorff space definition in terms of disconnected subsets

Published on 11 Jul 2015 - 9:08

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Proving that $(X,\tau)$ is Hausdorff given a condition.

Published on 13 Jul 2015 - 4:48

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Necessity of being Hausdorff in the definition of compactness?

Published on 13 Jul 2015 - 8:06

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Why (or when) is the direct limit of compact spaces paracompact?

Published on 17 Jul 2015 - 12:45

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Connected Lie group is second countable?

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Prove: the countable product of regular topological spaces is regular.

Published on 11 Aug 2015 - 11:36

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Alternative to dense subsets for non-Hausdorff spaces

Published on 12 Aug 2015 - 3:15

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How can I prove that $(X,τ)$ is a Hausdorff topological space?

Published on 26 Mar 2026 - 18:57

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Is it true that factor spaces are T4 if product space is T4?

Published on 27 Aug 2015 - 17:12

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An example of open closed continuous image of $T_0$-space that is not $T_0$

Published on 27 Aug 2015 - 18:16

List Question

$R_1$ paracompact spaces are normal

Proving that a compact subset of a Hausdorff space is closed

Compact Hausdorff spaces are normal

existence of functionals

Is the Alexandroff double circle compact and Hausdorff?

Hausdorff space definition in terms of disconnected subsets

Proving that $(X,\tau)$ is Hausdorff given a condition.

Necessity of being Hausdorff in the definition of compactness?

Why (or when) is the direct limit of compact spaces paracompact?

Connected Lie group is second countable?

Prove: the countable product of regular topological spaces is regular.

Alternative to dense subsets for non-Hausdorff spaces

How can I prove that $(X,τ)$ is a Hausdorff topological space?

Is it true that factor spaces are T4 if product space is T4?

An example of open closed continuous image of $T_0$-space that is not $T_0$

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