List questions from separation-axioms

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"internal" definition of complete regularity?

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Exercise in Section 2.4 of Singer & Thorpe

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A strong Hausdorff condition

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If a net converges in a weak Hausdorff space, then the limit point is unique

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If J is uncountable, then $R^J$ is not normal.

Published on 09 May 2014 - 5:42

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Being completely normal implies perfectly normal?

Published on 21 May 2014 - 18:31

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Let X be a complete metric space in which every closed ball is uncountable. Prove that X has cardinal number greater or equal than the continuum

Published on 06 Jun 2014 - 18:00

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Finer topologies on a compact Hausdorff space

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What application is there for a non-Hausdorff topological space?

Published on 17 Jun 2014 - 14:09

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With which separation axiom is the quotient space well-behaved?

Published on 23 Jun 2014 - 13:21

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Does paracompact Hausdorff imply perfectly normal?

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Product of $T_1$ spaces is $T_1$

Published on 18 Jul 2014 - 10:07

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T1 axiom in dual space

Published on 28 Jul 2014 - 12:45

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Constructing semi-regular spaces

Published on 29 Jul 2014 - 12:06

List Question

Give an example of non-normal subspace of a normal space.

"internal" definition of complete regularity?

Exercise in Section 2.4 of Singer & Thorpe

A strong Hausdorff condition

If a net converges in a weak Hausdorff space, then the limit point is unique

If J is uncountable, then $R^J$ is not normal.

Being completely normal implies perfectly normal?

Let X be a complete metric space in which every closed ball is uncountable. Prove that X has cardinal number greater or equal than the continuum

Finer topologies on a compact Hausdorff space

What application is there for a non-Hausdorff topological space?

With which separation axiom is the quotient space well-behaved?

Does paracompact Hausdorff imply perfectly normal?

Product of $T_1$ spaces is $T_1$

T1 axiom in dual space

Constructing semi-regular spaces

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