real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 12 years, 3 months ago Modified 1 year, 8 months ago
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 ...
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 …
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 < ∞.
Separability of $l^ {p}$ spaces - Mathematics Stack Exchange
Jul 21, 2015 · Explore related questions sequences-and-series functional-analysis metric-spaces lp-spaces separable-spaces
Is every Hilbert space separable? - Mathematics Stack Exchange
Sep 28, 2017 · From Wikipedia: A Hilbert space is separable if and only if it has a countable orthonormal basis. What are the examples of non-separable Hilbert spaces? From an applied point of view, are …
A very complete proof on the separability of $L^p$.
May 27, 2024 · Thm (2): $ (L^p (X, \Lambda, \mu), \| .\|_1)$ is separable iff $ (\Lambda_1, \rho_1)$ is separable. Addendum I read the link you added, i have two observation to do: My notion of …
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, 6 months ago Modified 6 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 - 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 …