Abstract
The study of two operators local function and the set operator $\psi$ on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp. $\psi$) and closure (local function) obey the relation $Int(A)$= X \ $Cl$(X \ A) (resp. $\psi$(A) = X \(X \A)$^*)$ . We search the general method of these relations, through this manuscript.
Highlights
Introduction and PreliminariesLet X be a set and }(X) be the power set of X
We introduce two new set operators on the ideal topological spaces
Detailed properties of these two operators are the part of this article
Summary
Let X be a set and }(X) be the power set of X. For the detail study of the local function, Natkaniec [18] had introduced another set operator which is called operator. This operator is de...ned as: for an ideal topological space G and for A X,. Int (A) = A \ (A) [2,5,14,16] This present paper has divided into two parts: one part is some new type of set operators on the ideal topological spaces and their relations. Characterizations of the Hayashi-Samuel spaces is included in this part The another part of this paper is related to the set-theory.
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