$\Psi_{\Gamma}-C$ Sets in Ideal Topological Spaces

Abstract

In this paper, we present a new type of set called $\Psi_{\Gamma}-C$ set by using the operator $\Psi_{\Gamma}$. We investigate the relationships of these sets with some special sets which were studied in the literature. For instance $\theta$-open set, semi $\theta$-open set, $\theta$-semiopen set, regular $\theta$-closed set. In particular, we show that $\Psi_{\Gamma}-C$ set is weaker than $\theta$-open set. Furthermore, we prove that the collection of $\Psi_{\Gamma}-C$ set is closed under arbitrary union. Finally, we obtain the conclusion that the collection of $\Psi_{\Gamma}-C$ set forms a supratopology.

Keywords

• $\Psi_{\Gamma}-C$ set
• local closure function
• $\theta$-closed set
• $L_{\Gamma}$-perfect set

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