Soft Generalized Closed Sets with Respect to an Ideal in Soft Topological Spaces

Abstract

Abstract:A soft ideal on a non empty set X is a non empty collection of soft subsets of X with heredity property which is also closed under finite unions. The concept of soft generalized closed sets in soft topological spaces was introduced by Kannan [1]. In this paper, we introduce and study the concept of soft generalized closed sets with respect to a soft ideal, which is the extension of the concept of soft generalized closed sets.

On soft regular generalized closed sets with respect to a soft ideal in soft topological spaces

“…Definition 2.23. [9,11] Let (X, ∼ τ, E) be a soft topological space over X, (F, E) and (G, E) soft sets over X. Two soft sets (F, E) and (G, E) are said to be soft disconnected sets if (F, E) − (G, E) = Φ and (G, E) − (F, E) = Φ.…”

“…[8] Every soft regular open set in a soft topological space (X, Definition 2.29. [9] A nonempty collection I of soft subsets over X is called a soft ideal on X if the following holds…”

“…They studied some basic properties of these concepts and investigated their relationships with different types of subsets of soft topological spaces with the help of counterexamples. Mustafa and Sleim [9] introduced the notion of a soft ideal in soft topological spaces. They introduced the concept of soft generalized closed sets with respect to a soft ideal and studied their properties in detail, which is extension of the concept of soft generalized closed sets.…”

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The notion of soft ideal in soft topological spaces was studied by Mustafa and Sleim [9]. They studied the concept of soft generalized closed sets with respect to a soft ideal, which is the extension of the concept of soft generalized closed sets.

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On Soft Turning Points

“…Mustafa el at. (9), presented the soft generalized closed sets and expand this idea into soft ideal topological spaces. In 2015 Aysequl and Goknur (10) introduced I_ regular, I_ normal and found a squire relations between them.…”