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
A reflexive Banach space is separable iff its dual is separable
Dec 12, 2014 · A reflexive Banach space is separable iff its dual is separable Ask Question Asked 11 years, 4 months ago Modified 11 years, 4 months ago
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?
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.
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 …
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
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 ...
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
functional analysis - $C (X)$ is separable when $X$ is compact ...
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 ...