List questions from separation-axioms

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271

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Closed surjection that does not preserve regularity

Published on 11 Aug 2014 - 8:36

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Show that $X$ is Hausdorff if and only if the diagonal $\Delta = \{(x, x):x \in X\}$ is closed in $X \times X$

Published on 19 Aug 2014 - 10:46

112

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Compact opens in sober $T_1$ are closed?

Published on 20 Aug 2014 - 9:47

251

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Showing that a space is normal and not locally compact

Published on 20 Aug 2014 - 20:32

755

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A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism

Published on 20 Aug 2014 - 20:55

411

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Infinite spaces in which all subsets are compact are not Hausdorff

Published on 21 Aug 2014 - 2:06

197

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If $(X,\tau)^n$ is Hausdorff, is $(X,\tau)$ also Hausdorff?

Published on 22 Aug 2014 - 6:34

76

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A countable, compact KC-subspace of a hereditarily Lindelöf minimal KC-space

Published on 22 Aug 2014 - 12:45

1.1k

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One-point sets are G$_\delta$ in first-countable $T_1$ spaces

Published on 25 Mar 2026 - 8:04

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Axioms of seperation

Published on 30 Aug 2014 - 17:45

68

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"Exemplary spaces" for the class of spaces satisfying separation axioms

Published on 04 Sep 2014 - 4:08

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Disjoint compact subsets of a Hausdorff space are separated by disjoint open neighborhoods

Published on 08 Sep 2014 - 12:11

481

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Clarification of Regular/Normal spaces discussion in Munkres

Published on 24 Sep 2014 - 19:19

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Proving that a compact space is regular

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List Question

Easier proof of "countable hypocompactness"

Closed surjection that does not preserve regularity

Show that $X$ is Hausdorff if and only if the diagonal $\Delta = \{(x, x):x \in X\}$ is closed in $X \times X$

Compact opens in sober $T_1$ are closed?

Showing that a space is normal and not locally compact

A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism

Infinite spaces in which all subsets are compact are not Hausdorff

If $(X,\tau)^n$ is Hausdorff, is $(X,\tau)$ also Hausdorff?

A countable, compact KC-subspace of a hereditarily Lindelöf minimal KC-space

One-point sets are G$_\delta$ in first-countable $T_1$ spaces

Axioms of seperation

"Exemplary spaces" for the class of spaces satisfying separation axioms

Disjoint compact subsets of a Hausdorff space are separated by disjoint open neighborhoods

Clarification of Regular/Normal spaces discussion in Munkres

Proving that a compact space is regular

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