Discontinuity points of separately continuous mappings with at most countable set of values

Abstract

UDC 517.51
We obtain a general result on the constancy of separately continuous mappings and their analogs, which implies the wellknown Sierpi´nski theorem. By using this result, we study the set of continuity points of separately continuous mappings with at most countably many values including, in particular, the mappings defined on the square of the Sorgenfrey line with values in the Bing plane.