Discontinuous strongly separately continuous functions of several variables and near coherence of two P-filters - Kozlovskyi, M. (Carpathian Mathematical Publications, 2024)
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 N_u 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=N_u_1×…×N_u_n we prove that the existence of a strongly separately continuous function f:X→R with one-point set {(u_1,…,u_n)} of discontinuity implies the existence of a strongly separately finite set EX such that the characteristic function χ|_E is discontinuous at (u_1,…,u_n). Using this fact we proved that the existence of a strongly separately continuous function f:X_1× …× X_n→R on the product of arbitrary completely regular spaces X_k with an one-point set {(x_1,…,x_n)} of points of discontinuity, where x_k is non-isolated G_δ-point in X_k, is equivalent to near coherence of P-filters.