real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 11 years, 11 months ago Modified 1 year, 4 months ago
Prove if $X$ is a compact metric space, then $X$ is separable.
Related: Prove that every compact metric space is separable (Although it seems that in that question the OP asks mainly about verification of their own proof.)
Prove that a subspace of a separable and metric space is itself separable
Prove that a subspace of a separable and metric space is itself separable Ask Question Asked 12 years, 3 months ago Modified 2 months ago
Definition of Separable Space - Mathematics Stack Exchange
Oct 8, 2020 · The standard definition (e.g. from wikipedia) that a separable topological space $X$ contains a countable, dense subset, or equivalently that there is a sequence $(x ...
real analysis - Is $L^p$ separable? - Mathematics Stack Exchange
Is Lp L p separable? Ask Question Asked 11 years, 6 months ago Modified 5 months ago
$C (X)$ is separable when $X$ is compact? - Mathematics Stack Exchange
Jun 19, 2015 · $X$ is a compact metric space, then $C(X)$ is separable, where $C(X)$ denotes the space of continuous functions on $X$. How to prove it? And if $X$ is just a compact ...
galois theory - The definition of the separable closure of a field ...
Mar 7, 2024 · Non-separable extensions and elements are not so nice in some ways, in particular recall that an extension is Galois if it is normal and separable. So one might consider only considering all …
A metric space is separable iff it is second countable
A metric space is separable iff it is second countable [closed] Ask Question Asked 12 years, 6 months ago Modified 9 years ago
general topology - Prove that $\mathbb {R}^k$ is separable ...
I'd like to show that $\\mathbb{R}^k$ is separable. (A metric space is called separable if it contains a countable dense subset.) Here's what I have and I'd like to confirm with everyone to see if
Every subspace of a separable metric space is separable.
Dec 2, 2017 · IIf it were right it would apply to every separable space because you have not used any of the metric properties. But a separable non-metrizable space can have a non-separable subspace.