The limiting oscillations of continuous functions

  • 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 $f$.

Article metrics
PDF downloads: 83
Abstract views: 229
How to Cite
(1)
Maslyuchenko O., Onypa D. The Limiting Oscillations of Continuous Functions. Carpathian Math. Publ. 2015, 7 (2), 191-196.