It is proved that if a function is continuous on an interval, then its variations on a set taken relative to some covering relations are also continuous as interval-functions. This result is applied to a direct construction of continuous Perron major and minor functions of Henstock integrable function.
"Continuity of δ-variation and construction of continuous major and minor functions for the Perron integral." Real Anal. Exchange 21 (1) 270 - 277, 1995/1996.