Some Topological and Cardinal Properties of the $$\boldsymbol{\lambda}_{\boldsymbol{\tau}}^{\boldsymbol{\varphi}}$$-Nucleus of a Topological Space $$\boldsymbol{X}$$

In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the $$\lambda_{\tau}^{\varphi}$$ -kernel of a topological space $$X$$ . It has been proved that the $$\lambda_{\tau}^{\varphi}$$ -kernel of a topological space $$X$$ preserves the density and the network $$\pi$$ -weight of normal spaces.

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