Discontinuous strongly separately continuous functions of several variables and near coherence of two -filters

Keywords:
separately continuous function, strongly separately continuous function, -filter, inverse problem, one-point discontinuityAbstract
We consider a notion of near coherence of -filters and show that the near coherence of any -filters is equivalent to the near coherence of any two -filters. For any filter on by we denote the space , in which all points from are isolated and sets , , are neighborhoods of . In the article, the concept of strongly separately finite sets was introduced. For we prove that the existence of a strongly separately continuous function with one-point set of discontinuity implies the existence of a strongly separately finite set such that the characteristic function is discontinuous at . Using this fact we proved that the existence of a strongly separately continuous function on the product of arbitrary completely regular spaces with an one-point set of points of discontinuity, where is non-isolated -point in , is equivalent to near coherence of -filters.