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.)
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 ...
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 …
The problem statement, all variables and given/known data: Show that if X is a subset of M and (M, d) is separable, then (X, d) is separable. [This may be a little bit trickier than it looks - E …
$X^*$ 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 ...
Is $L^p$ separable? - Mathematics Stack Exchange
Jun 27, 2014 · Wikipedia en.wikipedia.org/wiki/Separable_space#Non-separable_spaces: The Lebesgue spaces Lp, over a separable measure space, are separable for any 1 ≤ p < ∞.
Compositum of separable extension - Mathematics Stack Exchange
Apr 10, 2017 · From this, it follows that sums and products of separable elements are separable, and thus we have the claim: Compositums of separable extensions are separable.
Proving that a Banach space is separable if its dual is separable
Aug 10, 2017 · Proving that a Banach space is separable if its dual is separable Ask Question Asked 8 years, 4 months ago Modified 2 years, 1 month ago
functional analysis - Elegant proof that $L^2 ( [a,b])$ is separable ...
Apr 26, 2011 · The sub-$\mathbb Q$-vector space generated by the characteristic functions of intervals with rational end-points is countable and dense.