real analysis - Why is $\ell^\infty (\mathbb {N})$ not separable ...
My functional analysis textbook says "The metric space l∞ l ∞ is not separable." The metric defined between two sequences {a1,a2,a3 …} {a 1, a 2, a 3} and {b1,b2,b3, …} {b 1, b 2, b 3,} …
Prove if $X$ is a compact metric space, then $X$ is separable.
Related: Prove that every compact metric space is separable (Although it seems that in that question the OP asks mainly about verification of their own proof.)
Prove that a subspace of a separable and metric space is itself …
Prove that a subspace of a separable and metric space is itself separable Ask Question Asked 12 years, 3 months ago Modified 2 months ago
real analysis - Is $L^p$ separable? - Mathematics Stack Exchange
Is Lp L p separable? Ask Question Asked 11 years, 6 months ago Modified 5 months ago
functional analysis - $C (X)$ is separable when $X$ is compact ...
Jun 19, 2015 · this result is not trivial: If X is a compact T2 T 2 space X X, then C(X) C (X) is separable iff there is a metric X × X → R X × X → R that induces the topology of X X. You …
galois theory - The definition of the separable closure of a field ...
Mar 7, 2024 · Non-separable extensions and elements are not so nice in some ways, in particular recall that an extension is Galois if it is normal and separable. So one might consider only …
A metric space is separable iff it is second countable
A metric space is separable iff it is second countable [closed] Ask Question Asked 12 years, 6 months ago Modified 9 years 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 ...
Difference between separable and linear? Differentials
Mar 12, 2014 · This equation is a separable differential equations since we can rewrite this in the form of $\frac {dy} {y} = rdt$. Consider the fact that this is also a linear equation since $\frac …
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 …