List questions from separable-spaces

Published on 10 Feb 2023 - 12:04

102

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Topology question on first countable.

Published on 25 Mar 2026 - 11:08

88

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Prove that $X := \{ f: [0,1] \to [0,1] : f \text{ is continuous and } f(1) = 0 \}$ with the given distance is neither connected nor separable

Published on 24 Feb 2023 - 6:59

105

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Subspace of Euclidean space

Published on 26 Mar 2026 - 4:30

198

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Alternate proof of "$\ell^\infty$ is not separable".

Published on 05 Mar 2023 - 3:21

26

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$\forall r>0,j=1,2,\ldots:\mu(\partial B(x_j,r))=0$ for a Borel probability measure $\mu$ over a metric space $X$ where $x_j$ are countably dense

Published on 25 Mar 2026 - 17:26

136

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If $X$ is inseparable, must $Y$ be inseparable?

Published on 30 Mar 2023 - 13:42

38

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Why the metric space $(\mathbb{D}(\mathbb{R}^d),\delta_{lu})$ is not separable?

Published on 10 Apr 2023 - 18:08

72

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Prove that, an atomic/purely atomic measure on a separable metric space is supported by a countable set

Published on 28 Apr 2023 - 6:49

130

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Is $C^\infty([0,1]^n)$ a separable Frechet space?

Published on 09 May 2023 - 16:03

58

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Separable space, the countable dense sequence, and it's index family

Published on 22 May 2023 - 19:22

117

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A metric space is separable if and only if it is homeomorphic to a totally bounded metric space

Published on 28 May 2023 - 3:14

65

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$H=\bigoplus H_n$ is separable?

Published on 29 May 2023 - 3:17

110

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Continuous tensor products

Published on 07 Jun 2023 - 18:10

37

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Infinite intersection of closed Hilbert subspaces whose finite intersection is infinite-dimensional

Published on 08 Jun 2023 - 8:30

List Question

Density of functions in "increasing pointwise" sense

Topology question on first countable.

Prove that $X := \{ f: [0,1] \to [0,1] : f \text{ is continuous and } f(1) = 0 \}$ with the given distance is neither connected nor separable

Subspace of Euclidean space

Alternate proof of "$\ell^\infty$ is not separable".

$\forall r>0,j=1,2,\ldots:\mu(\partial B(x_j,r))=0$ for a Borel probability measure $\mu$ over a metric space $X$ where $x_j$ are countably dense

If $X$ is inseparable, must $Y$ be inseparable?

Why the metric space $(\mathbb{D}(\mathbb{R}^d),\delta_{lu})$ is not separable?

Prove that, an atomic/purely atomic measure on a separable metric space is supported by a countable set

Is $C^\infty([0,1]^n)$ a separable Frechet space?

Separable space, the countable dense sequence, and it's index family

A metric space is separable if and only if it is homeomorphic to a totally bounded metric space

$H=\bigoplus H_n$ is separable?

Continuous tensor products

Infinite intersection of closed Hilbert subspaces whose finite intersection is infinite-dimensional

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