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
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 < ∞.
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 ...
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 …
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.
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 …
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