List questions from separable-spaces

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How close is a countable generator related to separability?

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Separability of Banach space.

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Prove that $C_0(X)$ is separable given that X is locally compact metric space

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Separating hyperplane from a set to an outer point

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Prove that $f(A)$ is a separable subset

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Let $X$ and $Y$ be separable metric spaces and let $S$ be a subset of $X$. Show that the space $S$ is separable

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Classifying Hausdorff spaces

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Non-separable Hilbert space

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How big can a separable Hausdorff space be?

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$(\ell_p,\|\cdot\|_{\infty})$ Banach or separable

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Give an example of a non-separable subspace of a separable space

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Non-separable compact space

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902

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How can I show that $L^{1}([0,1])$ is a separable metric space?

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Topological counterexample: compact, Hausdorff, separable space which is not first-countable

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List Question

Countable union of compact sets is separable?

How close is a countable generator related to separability?

Separability of Banach space.

Prove that $C_0(X)$ is separable given that X is locally compact metric space

Separating hyperplane from a set to an outer point

Prove that $f(A)$ is a separable subset

Let $X$ and $Y$ be separable metric spaces and let $S$ be a subset of $X$. Show that the space $S$ is separable

Classifying Hausdorff spaces

Non-separable Hilbert space

How big can a separable Hausdorff space be?

$(\ell_p,\|\cdot\|_{\infty})$ Banach or separable

Give an example of a non-separable subspace of a separable space

Non-separable compact space

How can I show that $L^{1}([0,1])$ is a separable metric space?

Topological counterexample: compact, Hausdorff, separable space which is not first-countable

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