Abstract
In this paper we introduce a new class of semi generalized open sets, generalized semi closed sets in topological spaces, and studied some of its basic properties. Moreover we define approximately semi generalized open sets and approximately generalized semi closed sets in topological spaces. Further we obtained some properties of closure, semi generalized open sets and generalized semi closed sets in topological spaces.
Highlights
The study of generalized closed sets in topological space was initiated by Levine in [23]
The aim of this paper is to introduce the concept of semi generalized open Sets and generalized semi closed Sets in topological spaces, and provide Semi generalized open Sets and generalized semi closed Sets in topological spaces
A subset A of a topological space (X, τ) is said to be (i) a semi – open set [9] if A ⊆ cl(int(A)) and a semi closed if int(cl(A)) ⊆ A, (ii) a preopen set [11] if A ⊆ int(cl(A)) and a pre closed if cl(int(A)) ⊆ A, (iii) an ∝ - open sets [12] if A ⊆ int (cl(int(A))) and ∝ - closed sets if cl (int(cl(A))) ⊆ A, (iv) A regular set [13] if int(cl(A)) = A and a regular closed set if cl(int(A)) = A, (v) A Q – set [10] if cl(int(A)) = int(cl(A))
Summary
The study of generalized closed sets in topological space was initiated by Levine in [23]. Topology is an important and interesting area of mathematics, the study of which will introduce to new concepts and theorems and put into context old ones like continuous functions [1]. It is so fundamental that its influence is evident in almost every other branch of mathematics [3]. Topological notions like compactness, connectedness and denseness areas basic to mathematicians of today as sets and functions were. Topological spaces; semi generalized open sets; semi generalized closed sets. Topology has several different branches, genera l topology, algebraic topology, differential topology and topological algebra, the first, general topology, being the door to the study of the others [3,5]. The aim of this paper is to introduce the concept of semi generalized open Sets and generalized semi closed Sets in topological spaces, and provide Semi generalized open Sets and generalized semi closed Sets in topological spaces
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