The limiting oscillations of continuous functions

O. V. Maslyuchenko, D. P. Onypa

Abstract


We prove that for any upper semicontinuous function $f:F\rightarrow [0;+\infty]$ defined on the boundary $F=\overline G\setminus G$ of some open set $G$ in metrizable space $X$ there is a continuous function $g:G\rightarrow \mathbb R$ such that the limiting oscillation $\widetilde \omega_g$ of it equals $f$.

Keywords


limiting oscillation, discreetly attainable space, upper semicontinuous function

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