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 ...

Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 12 years, 2 months ago Modified 1 year, 7 months ago

Jul 21, 2015 · Explore related questions sequences-and-series functional-analysis metric-spaces lp-spaces separable-spaces

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 …

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 Ask Question Asked 12 years, 6 months ago Modified 6 months ago

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 Ask Question Asked 14 years, 5 months ago Modified 7 years, 9 months ago

Apr 26, 2011 · The sub-$\mathbb Q$-vector space generated by the characteristic functions of intervals with rational end-points is countable and dense.

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 …