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

Authors

https://doi.org/10.15330/cmp.16.2.469-483

Keywords:

separately continuous function, strongly separately continuous function, P-filter, inverse problem, one-point discontinuity
Published online: 2024-11-08

Abstract

We consider a notion of near coherence of n P-filters and show that the near coherence of any n P-filters is equivalent to the near coherence of any two P-filters. For any filter u on N by Nu we denote the space N{u}, in which all points from N are isolated and sets A{u}, Au, are neighborhoods of u. In the article, the concept of strongly separately finite sets was introduced. For X=Nu1××Nun we prove that the existence of a strongly separately continuous function f:XR with one-point set {(u1,,un)} of discontinuity implies the existence of a strongly separately finite set EX such that the characteristic function χ|E is discontinuous at (u1,,un). Using this fact we proved that the existence of a strongly separately continuous function f:X1××XnR on the product of arbitrary completely regular spaces Xk with an one-point set {(x1,,xn)} of points of discontinuity, where xk is non-isolated Gδ-point in Xk, is equivalent to near coherence of P-filters.

How to Cite
(1)
Kozlovskyi, M. Discontinuous Strongly Separately Continuous Functions of Several Variables and Near Coherence of Two P-Filters. Carpathian Math. Publ. 2024, 16, 469-483.