real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 11 years, 10 months ago Modified 1 year, 3 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 ...
functional analysis - $C (X)$ is separable when $X$ is compact ...
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 ...
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, 2 months ago Modified 2 months ago
$X^*$ is separable then $X$ is separable [Proof explanation]
Feb 5, 2020 · $X^*$ is separable then $X$ is separable Proof: Here is my favorite proof, which I think is simpler than both the one suggested by David C. Ullrich and the one I had ...
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, 5 months ago Modified 8 years, 11 months ago
real analysis - Is $L^p$ separable? - Mathematics Stack Exchange
Is Lp L p separable? Ask Question Asked 11 years, 5 months ago Modified 5 months ago
galois theory - The definition of the separable closure of a field ...
Mar 7, 2024 · In any case, each polynomial that has a zero in the separable closure will also decompose in linear factors; thus ext. is normal. Also, note that for some fields such as the rationals or any field …
Proving that a Banach space is separable if its dual is separable
Aug 10, 2017 · $ \mathbb R $ is separable normed space. Is the set of irrational numbers separable in the subspace topology?