Discontinuous Separately Continuous Functions and Near Coherence of P-Filters

Abstract

We prove that the problem of the existence of a discontinuous separately continuous function $f:X \times Y\to\mathbb{R}$ for any non-discrete Tychonov spaces $X,\,Y$ of countable pseudocharacter is equivalent to NCPF (Near Coherence of $P$-filters) which is independent of ZFC. Also for every non-discrete Tychonov space $X$ we find an abelian topological group $G$ of countable cellularity and a discontinuous separately continuous function $f:X \times G \to\mathbb{R}$.