In this paper we study the behavior of some properties of topological spaces under the influence of the N-tau(phi)-kernel of a space X. We prove that the N-tau(phi)-kernel of a space Xpreserves the density, network and pi-weight of normal spaces. Besides, it is shown that the N-compact kernel of a space Xpreserves the Souslin number, weight, density, and pi-network weight of normal spaces. (c) 2023 Elsevier B.V. All rights reserved.