The limiting oscillations of continuous functions - Maslyuchenko, O.V.; Onypa, D.P. (Carpathian Mathematical Publications, 2015)
We prove that for any upper semicontinuous function f:F→ [0;+∞] defined on the boundary F=GG of some open set G in metrizable space X there is a continuous function g:G→ R such that the limiting oscillation ω_g of it equals f.