Characterization of Two Specific Cases with New Operators in Ideal Topological Spaces

Abstract

This research deals with new operators $\wedge_{\Gamma}$, $\veebar_{\Gamma}$, and $\barwedge_{\Gamma}$, defined using $\Gamma$-local closure function and $\Psi_{\Gamma}$-operator in ideal topological spaces. It investigates the main features of these operators and their relationships with each other. The paper also analyzes their behaviors in some special ideals. Besides, it explores whether these operators preserve some set operations. Then, the study researches the properties of some special sets using these operators and proposes their characterizations. Additionally, it interprets some characterizations of the case cl$(\tau)\cap \Im=\{\emptyset\}$ and the closure compatibility by means of these new operators.

Keywords

• Ideal
• $\Gamma$-local closure function
• $\Psi_{\Gamma}$-operator

Supporting Institution

The Office of Scientific Research Projects Coordination at Canakkale Onsekiz Mart University

Project Number

FHD-2023-4505

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