Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 12 years, 1 month ago Modified 1 year, 6 months ago

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 ...

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 < ∞.

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

Prove that a subspace of a separable and metric space is itself separable Ask Question Asked 12 years, 5 months ago Modified 5 months ago

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 ...

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

Feb 5, 2020 · $X^*$ is separable then $X$ is separable [Proof explanation] Ask Question Asked 6 years, 1 month ago Modified 6 years, 1 month 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...

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 …