Some topological and cardinal properties of the NτΦ-nucleus of a space X.

In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the NτΦ-kernel of a space X. It has been proved that the NτΦ-kernel of a space X preserves the density and the network p - weight of normal spaces. Besides, shown that the N-compact kernel of a space X preserves the Souslin properties, the weight, the density, and the p-network weight of normal spaces. [ABSTRACT FROM AUTHOR]