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 < ∞.
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 …
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
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 5 months ago
Proof of separability of $L^p$ spaces - Mathematics Stack Exchange
A metrizable space is separable if and only if it is second-countable. This means that the euclidean topology on $\mathbb {R}^n$ has a countable basis. This countable basis is explicitely described in …
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 …
I would like to show that $\\ell^1$ is separable
So here is my question, I want to prove that $\\ell^1$ is separable. So i need to show that there exists a countable dense subset in $\\ell^1$. Since I am not sure if my idea was right i hoped som...
Prove that $X^\\ast$ separable implies $X$ separable
Prove that $X^\ast$ separable implies $X$ separable Ask Question Asked 14 years, 4 months ago Modified 7 years, 9 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 ...
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.