List questions from separation-axioms

Published on 19 Jan 2011 - 16:06

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Completely separated sets, Stone–Čech compactification

Published on 20 Jan 2011 - 6:55

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Example of Hausdorff space $X$ s.t. $C_b(X)$ does not separate points?

Published on 27 Feb 2011 - 13:36

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Urysohn's function on a metric space

Published on 24 Jun 2011 - 8:22

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Quotient Space of Hausdorff space

Published on 07 Jul 2011 - 7:18

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Is the set of fixed points in a non-Hausdorff space always closed?

Published on 05 Aug 2011 - 17:55

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If every continuous $f:X\to X$ has $\text{Fix}(f)\subseteq X$ closed, must $X$ be Hausdorff?

Published on 05 Aug 2011 - 19:17

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Why are these two definitions of a perfectly normal space equivalent?

Published on 12 Oct 2011 - 21:47

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Does perfectly normal $\implies$ normal?

Published on 13 Oct 2011 - 7:49

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Is a metric space perfectly normal?

Published on 18 Oct 2011 - 9:28

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How to prove that a compact set in a Hausdorff topological space is closed?

Published on 18 Nov 2011 - 12:46

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$X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$

Published on 15 Dec 2011 - 2:10

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Diagonal $\Delta = \{x \times x : x \in X \}$ closed in $X \times X$ implies that $X$ is Hausdorff

Published on 27 Mar 2026 - 11:48

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An inductive construct of the Hausdorff reflection

Published on 15 Mar 2012 - 20:06

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Product of two regular spaces

Published on 27 Mar 2026 - 13:18

List Question

Regular but not normal space

Completely separated sets, Stone–Čech compactification

Example of Hausdorff space $X$ s.t. $C_b(X)$ does not separate points?

Urysohn's function on a metric space

Quotient Space of Hausdorff space

Is the set of fixed points in a non-Hausdorff space always closed?

If every continuous $f:X\to X$ has $\text{Fix}(f)\subseteq X$ closed, must $X$ be Hausdorff?

Why are these two definitions of a perfectly normal space equivalent?

Does perfectly normal $\implies$ normal?

Is a metric space perfectly normal?

How to prove that a compact set in a Hausdorff topological space is closed?

$X/{\sim}$ is Hausdorff if and only if $\sim$ is closed in $X \times X$

Diagonal $\Delta = \{x \times x : x \in X \}$ closed in $X \times X$ implies that $X$ is Hausdorff

An inductive construct of the Hausdorff reflection

Product of two regular spaces

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