OSCILLATION AND ω-PRIMITIVES
OSCILLATION AND ω-PRIMITIVES
We extend the results of [2], [6] in the case of topological spaces. It is shown that given an upper semicontinuous (USC) function $f:X\to [0,\infty)$ where $X$ is a massive first countable $T_1$-space satisfying some "neighborhood conditions", there exists $F:X\to [0, \infty)$ whose oscillation equals $f$ everywhere on $X$ (Theorem …