Abstract
The purpose of this paper is to introduce and study a new class of generalized closed sets in a topological space X, defined in terms of a grill G on X. Explicit characterization of such sets along with certain other properties of them are obtained. As applications, some characterizations of regular and normal spaces are achieved by use of the introduced class of sets.
Highlights
We introduce and study a new class of generalized closed sets, termed G-g-closed, in terms of a given grill G on the ambient space, the definition having a close bearing to the above operator Φ
We begin by introducing a new class of generalized closed sets in terms of grills as follows
Remark 2.5 In the case of principal grill [X] generated by X, it is known [10] that τ = τ[X], so that any [X]-g-closed set becomes a g-closed set and vice-versa
Summary
We introduce and study a new class of generalized closed sets, termed G-g-closed, in terms of a given grill G on the ambient space, the definition having a close bearing to the above operator Φ. Theorem 2.7 Let (X, τ ) be a topological space and G be a grill on X. Corollary 2.10 Let G be grill on a space (X, τ ) and A be a G-g-closed set.
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