real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
Why is $\ell^\infty (\mathbb {N})$ not separable? Ask Question Asked 12 years, 2 months ago Modified 1 year, 7 months ago
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
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 …
Proving that a Banach space is separable if its dual is separable
Aug 10, 2017 · $ \mathbb R $ is separable normed space. Is the set of irrational numbers separable in the subspace topology?
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 …
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 subspace.
Why is a field extension separable if and only if the discriminant of ...
Nov 20, 2022 · Why is a field extension separable if and only if the discriminant of the basis of the field extension is nonzero? Ask Question Asked 3 years, 4 months ago Modified 3 years, 4 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 < ∞.
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 …
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 ...