All Questions

It is well known that a separable space is a topological space that has a countable dense subset. I am wondering how is this related to the name 'separable'? Any intuition where the name come from?

If $X$ is a set (feel free to think of it as finite, but it doesn't have to be) and $f$ a real function on $X$, call the support $\operatorname{supp} f$ the subset of $X$ consisting of all elements $i\...

Let $X = C(\mathbb R)$ be the Fréchet space of real-valued continuous functions. For each $f \in X$ and each compact set $D \subseteq \mathbb R$, let $$[f]_D = \{ g \in X : \mbox{$g(t) = f(t)$ for ...

In the context of Banach space theory, what is the correct terminology: extremally disconnected or extremely disconnected. Looking through the internet I have met using both extremely and extremally ...