List questions from separable-spaces

Published on 14 Mar 2022 - 10:07

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Why is $\inf_{h \in E^\star}\{\|f-h\|_1+[h]^2\}= \min _{h \in E^\star} \{\|f-h\|_1^2+[h]^2\}$ in Brezis's solution of Ex 3.27.4?

Published on 17 Mar 2022 - 21:22

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Apparent contradiction between weak metrizability results

Published on 23 Feb 2026 - 8:36

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Reflexivity and Separability of $L^{\infty}$ and $L^{1}$

Published on 23 Feb 2026 - 11:48

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Prove that $A(\Delta)$ is a separable space

Published on 01 Apr 2022 - 15:23

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The Span of a Countable Set is always Separable?

Published on 05 Apr 2022 - 1:05

368

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Every normed space with countable dimension is separable.

Published on 07 Apr 2022 - 16:00

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Constructing sequence of nested closed sets in separable $T_{3\frac 1 2}$ space

Published on 23 Feb 2026 - 6:20

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Borel $\sigma$-algebra of separable $T_{3 \frac 1 2 }$ space generated by bounded continuous functions

Published on 23 Feb 2026 - 6:22

193

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Intersection of separable metric spaces endowed with the sum of metrics

Published on 11 Apr 2022 - 9:36

250

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An easy question about the separability of $L^p(X,\mathcal{A}, \mu)$ space, where $p\in [1,+\infty)$

Published on 20 Apr 2022 - 19:04

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Is Probability Measure always tight?

Published on 24 Apr 2022 - 6:47

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Metric space $(X,d)$ is separable if and only if $(X,m)$ is separable, where $ad(x,y)\le m(x,y) \le bd(x,y)$ for any $x,y \in X$ and $a,b>0$.

Published on 26 Apr 2022 - 14:18

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Every open subspace of a separable topological space is separable

Published on 27 Apr 2022 - 15:56

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Exercise 10, Section 30 of Munkres’ Topology

Published on 28 Apr 2022 - 19:35

List Question

Can this set be not separable ? Can it be not compact?

Why is $\inf_{h \in E^\star}\{\|f-h\|_1+[h]^2\}= \min _{h \in E^\star} \{\|f-h\|_1^2+[h]^2\}$ in Brezis's solution of Ex 3.27.4?

Apparent contradiction between weak metrizability results

Reflexivity and Separability of $L^{\infty}$ and $L^{1}$

Prove that $A(\Delta)$ is a separable space

The Span of a Countable Set is always Separable?

Every normed space with countable dimension is separable.

Constructing sequence of nested closed sets in separable $T_{3\frac 1 2}$ space

Borel $\sigma$-algebra of separable $T_{3 \frac 1 2 }$ space generated by bounded continuous functions

Intersection of separable metric spaces endowed with the sum of metrics

An easy question about the separability of $L^p(X,\mathcal{A}, \mu)$ space, where $p\in [1,+\infty)$

Is Probability Measure always tight?

Metric space $(X,d)$ is separable if and only if $(X,m)$ is separable, where $ad(x,y)\le m(x,y) \le bd(x,y)$ for any $x,y \in X$ and $a,b>0$.

Every open subspace of a separable topological space is separable

Exercise 10, Section 30 of Munkres’ Topology

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