All Questions

It is well known that a regular space is a topological space $X$ with these two properties: 1)All one point sets are closed. 2)For every $x\in X$ and every closed set $B$ (such that $x\notin B$), ...

A mob is a word used for a topological semigroup which is a Hausdorff space. A clan is a compact connected mob with a two-sided identity element. Who used these words with these meanings first and ...

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?