The limiting oscillations of continuous functions

O.V. Maslyuchenko; D.P. Onypa

doi:10.15330/cmp.7.2.191-196

The limiting oscillations of continuous functions

Authors

O.V. Maslyuchenko Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine
D.P. Onypa Yuriy Fedkovych Chernivtsi National University, 2 Kotsjubynskyi str., 58012, Chernivtsi, Ukraine

https://doi.org/10.15330/cmp.7.2.191-196

Keywords:

limiting oscillation, discreetly attainable space, upper semicontinuous function

Published online: 2015-12-14

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 $f$ .