ИСТИНА

Let X and Y be countably compact spaces, Z be a space, and f : X × Y → Z be a separately continuous mapping. If Z is a Tychonoff space, then there is a compact extension bX of X, such that the mapping f extends to a separately continuous mapping f ˆ : bX × Y → βZ , where βZ is the Stone–Cech compactification of Z. The paper discusses under what conditions there exist extensions bX and bZ of the spaces X and Y, respectively, such that the mapping f extends to a separately continuous mapping f ˆ : bX × Y → bZ. The application of the obtained results to the problem of continuity of operations in groups with topology is considered.