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.)
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 ...
Prove that a subspace of a separable and metric space is itself …
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
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 …
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 …
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
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 …
general topology - Separable implies second countable
Start asking to get answers Find the answer to your question by asking. Ask question general-topology separable-spaces second-countable