Let $X$ and $Y$ be metric spaces and $f: X \rightarrow Y$ a Borel measurable function. Does $f$ have to be of bounded class, i.e. are the sets $f^{-1}\lbrack H ...

If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...