Unified theory of the kernel of a set via hereditary classes and generalized topologies

José Sanabria; Laura Maza; Ennis Rosas; Carlos Carpintero

doi:10.35834/2023/3501060

Abstract

We build a unification of several variants of the kernel of a set in a generalized topological space endowed with a hereditary class, which is a fundamental concept to introduce new modifications of important concepts as open sets and closed sets. This new theoretical framework leads to the study in unified form of separation properties in a context much more general and versatile than the case of a topological space provided with an ideal.

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José Sanabria. Laura Maza. Ennis Rosas. Carlos Carpintero. "Unified theory of the kernel of a set via hereditary classes and generalized topologies." Missouri J. Math. Sci. 35 (1) 60 - 74, May 2023. https://doi.org/10.35834/2023/3501060

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Published: May 2023

First available in Project Euclid: 7 June 2023

MathSciNet: MR4598387

Digital Object Identifier: 10.35834/2023/3501060

Subjects:

Primary: 54A05

Secondary: 54A10 , 54D10

Keywords: $(\mu^{\star}\mu^{\bullet})$-$T_{1/2}$ space , $\mathcal{H}$-$g\Lambda_{\mu}$-set , $\mu$-kernel , $\mu^{\bullet}$-closed set , function $A^{\bullet}_{\mu}(\mathcal{H})$ , generalized topology , hereditary class

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