All Questions

Everyone knows the Heine-Borel theorem characterizing compact subsets of Euclidean space. For any $n \in \mathbb N$ a set $A \subseteq \mathbb R^n$ is compact just in case it is closed and bounded (in ...

I’m wondering if there is a version of Arzelà-Ascoli for continuous functions on not-necessarily compact metric/Hausdorff spaces $X$, i.e. a characterization of the compact subsets of $C_b(X)$ (under ...

Suppose $X$ is a locally compact Hausdorff space. Define the Baire sets in $X$, denoted by $\mathcal Ba(X)$, to be the smallest $\sigma$-algebra that contains all compact $G_\delta$ subsets of $X$. ...