List questions from separation-axioms

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Image of a normal space under a closed and continuous map is normal

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Cantor cubes are universal for totally disconnected compact Hausdorff spaces

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If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed

Published on 23 Jan 2013 - 23:10

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Base for a topology, euclidean topology and Hausdorff

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Showing that a space is completely normal iff every subspace is normal

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

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Suppose every complete subset of a uniform space is closed. Is it Hausdorff?

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Singleton closure in Hausdorff spaces.

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Is the closure of a Hausdorff space, Hausdorff?

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Compactness and Strictly Finer Topologies.

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Prove that $Y$ is Hausdorff iff $X$ is Hausdorff and $A$ is a closed subset of $X$

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Proof of Equivalent Characterisation of Complete Metric Space without using Compactifications

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CW complexes are T$_1$

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List Question

How to show that topological groups are automatically Hausdorff?

Image of a normal space under a closed and continuous map is normal

Cantor cubes are universal for totally disconnected compact Hausdorff spaces

If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed

Base for a topology, euclidean topology and Hausdorff

Showing that a space is completely normal iff every subspace is normal

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

Suppose every complete subset of a uniform space is closed. Is it Hausdorff?

Singleton closure in Hausdorff spaces.

Is the closure of a Hausdorff space, Hausdorff?

Why are ordered spaces normal? [collecting proofs]

Compactness and Strictly Finer Topologies.

Prove that $Y$ is Hausdorff iff $X$ is Hausdorff and $A$ is a closed subset of $X$

Proof of Equivalent Characterisation of Complete Metric Space without using Compactifications

CW complexes are T$_1$

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