List questions from lindelof-spaces

Published on 22 Feb 2026 - 23:29

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Show that if a topological space has at most countable basis, then the space is separable and Lindelöf

Published on 22 Feb 2026 - 21:31

620

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Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.

Published on 22 Feb 2026 - 23:28

54

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Show that a Regular space $X$ is Lindelöf if it has a locally finite open cover $\mathcal{U}$ such that $\rm{Fr}\,U$ has the Lindelöf property

Published on 22 Feb 2026 - 23:29

184

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Proof for $\mathbb{R}_{l}$ is Lindelof

Published on 22 Feb 2026 - 23:27

1.3k

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Lindelöf and separable metric space

Published on 22 Feb 2026 - 23:27

61

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Countable $\varepsilon$-net of measurable sets

Published on 22 Feb 2026 - 23:25

186

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Munkres 37.3 maximal set with respect to the countable intersection property.

Published on 22 Feb 2026 - 23:26

121

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Almost Lindelöf spaces.

Published on 22 Feb 2026 - 23:25

2.4k

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How to show $R_l$ is Lindelöf space?

Published on 22 Feb 2026 - 23:29

135

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Classifying Hausdorff spaces

Published on 22 Feb 2026 - 23:23

1.6k

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Lindelöf if and only if every collection with the countable intersection property has non-empty intersection of closures

Published on 23 Feb 2026 - 1:22

2k

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Lindelöf and second countable spaces

Published on 23 Feb 2026 - 1:18

202

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Second Countability $\implies$ Lindelöf property(Proof verification)

Published on 23 Feb 2026 - 1:18

66

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$Y\subset X$ is Lindelof iff Every $X$-open cover of $Y$ has a countable $X$-open subcover.

Published on 23 Feb 2026 - 1:23

List Question

Proof by Contradiction--Product of Lindelöf Spaces is Lindelöf

Show that if a topological space has at most countable basis, then the space is separable and Lindelöf

Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.

Show that a Regular space $X$ is Lindelöf if it has a locally finite open cover $\mathcal{U}$ such that $\rm{Fr}\,U$ has the Lindelöf property

Proof for $\mathbb{R}_{l}$ is Lindelof

Lindelöf and separable metric space

Countable $\varepsilon$-net of measurable sets

Munkres 37.3 maximal set with respect to the countable intersection property.

Almost Lindelöf spaces.

How to show $R_l$ is Lindelöf space?

Classifying Hausdorff spaces

Lindelöf if and only if every collection with the countable intersection property has non-empty intersection of closures

Lindelöf and second countable spaces

Second Countability $\implies$ Lindelöf property(Proof verification)

$Y\subset X$ is Lindelof iff Every $X$-open cover of $Y$ has a countable $X$-open subcover.

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