Abstract
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 π - 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 π -network weight of normal spaces.
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