List questions from separation-axioms

88

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Is there a first countable, $T_1$, weakly Lindelof, sequentially compact space which is not also compact?

Published on 23 Feb 2026 - 5:18

51

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Strong Seperation between hypreplane and an affine subspace

Published on 26 Mar 2026 - 14:42

69

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How to prove that he looped line topology is Tychonoff?

Published on 23 Feb 2026 - 6:23

318

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Does a metric space need to be a Hausdorff space?

Published on 23 Mar 2024 - 2:44

3k

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Question about quotient of a compact Hausdorff space

Published on 06 Jan 2015 - 18:56

144

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Exam preparation: Topological embedding from a Hausdorff space

Published on 07 Jan 2015 - 21:02

43

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How to find a hyperplane

Published on 21 Jan 2015 - 11:42

2.3k

Views

Polynomial Functions separate points

Published on 02 Feb 2015 - 21:27

357

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First examples for topology of non-Hausdorff spaces

Published on 05 Feb 2015 - 1:15

55

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Compactness and open sets

Published on 03 Mar 2015 - 19:09

48

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Are $\{(x,0) \in \mathbb{R^2} : x \in \mathbb{R}\}$ and $\{(x,\frac{1}{x}) : x >0\}$ separated?

Published on 12 Mar 2015 - 1:44

50

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Example of a connected set where $\exists r>0$ such that $d(a,b) \geq r$, $\forall a \in A$, $\forall b \in B$

Published on 13 Mar 2015 - 12:35

2.7k

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Every order topology is regular (proof check)

Published on 23 Feb 2026 - 8:36

54

Views

How to show $\mathbb{R^2}$ is sequentially connected without path-connectedness

Published on 22 Mar 2015 - 13:36

211

Views

Set-theoretic intersection of affine open subschemes.

Published on 29 Mar 2015 - 13:56

List Question

Is there a first countable, $T_1$, weakly Lindelof, sequentially compact space which is not also compact?

Strong Seperation between hypreplane and an affine subspace

How to prove that he looped line topology is Tychonoff?

Does a metric space need to be a Hausdorff space?

Question about quotient of a compact Hausdorff space

Exam preparation: Topological embedding from a Hausdorff space

How to find a hyperplane

Polynomial Functions separate points

First examples for topology of non-Hausdorff spaces

Compactness and open sets

Are $\{(x,0) \in \mathbb{R^2} : x \in \mathbb{R}\}$ and $\{(x,\frac{1}{x}) : x >0\}$ separated?

Example of a connected set where $\exists r>0$ such that $d(a,b) \geq r$, $\forall a \in A$, $\forall b \in B$

Every order topology is regular (proof check)

How to show $\mathbb{R^2}$ is sequentially connected without path-connectedness

Set-theoretic intersection of affine open subschemes.

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