real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 12 years ago Modified 1 year, 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 ...
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 ...
$X^*$ 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 < ∞.
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, 4 months ago Modified 4 months 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.
functional analysis - Separable Banach Spaces vs. Non-separable ones ...
Oct 13, 2017 · I have just learned about separable Banach spaces. The definition of a separable space that I know is that a space is separable if you can find a countable dense subset of it. I would be …
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?
A subspace of a separable space is not necessarily seperable
Apr 6, 2021 · This topological space is separable because $\ {x\}$ is a countable dense subset. However the subspace topology on $\mathbb R$ is not,because it is the discrete topology.