Abstract
In this paper we introduce and study the concept of Ss-open sets .also, a study new class of functions called Ss-continuous functions, the relationships between Ss-continuity and other types of continuity are investigated. Keywords: Ss-open set, Ss-continuous function, semi-open set, semi-continuous functions.
Highlights
In 1963, Levine [16], introduced the concept of semi-open set and semi continuity and gave several properties about these functions
In this paper we introduce and study the concept of Ss-open sets .a study new class of functions called SScontinuous functions, the relationships between Ss-continuity and other types of continuity are investigated
Njastad [18] introduced the concepts of α-sets and Abd-El-Monsef et al [1] defined β-open sets and β-continuous functions
Summary
In 1963, Levine [16], introduced the concept of semi-open set and semi continuity and gave several properties about these functions. A subset A is said to be preopen [17] (resp., α-open [18], semi-open [16], regular open [21], β-open [1]) set if A ⊆ IntCl(A) The complement of a preopen (resp., α-open , semi-open , regular open, β-open) set is called pre-closed (resp., α-closed, semi-closed, regular closed, β-closed) set. A subset A of a topological space X is said to be regular-semi-open [4] if there exists a regular-open set U such that U ⊆ A ⊆ ClU equivalently A is regular-semi-open [22] if and only if A = sIntsClA. Since the families SO(X) and P O(X) are incomparable [17], so the it is obvious that the concept of Ss-open sets incomparable with Sp-open sets but it is strictly weaker than Sc-open sets and stronger than Sβ-open sets
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