δ(δg)*-Closed sets in Topological Spaces

Abstract

In this paper we introduce and study a new class of generalised closed sets called δ(δg)*-closed sets in topological spaces using δg-closed sets. Moreover we analyse the relations between δ(δg)*-closed sets and already existing various closed sets. It is independent of δg-closed sets and weaker than δg*-closed sets. The class of δ(δg)*- closed sets is properly placed between the classes of δg*-closed sets and δg# -closed sets and a chain of relations is proved as follows. r-closed  π-closed  δ-closed  δg*-closed  δ(δg)*-closed  δg#-closed  gδ-closed

Keywords

g-closed sets, δg-closed sets , δg*-closed sets and δ(δg)*-closed sets.

I. INTRODUCTION

II.PRELIMINARIES

The complements of the above mentioned sets are called regular closed, semi closed, - closed, pre- closed, Semi pre closed, π-closed and δ-closed sets respectively.

The intersection of all regular closed(resp.semi-closed ,-closed, pre-closed, semi pre-closed, π-closed and δ-closed) subsets of (X, ) containing A is called the regular closure(resp.semi-closure, -closure, pre- closure, semi pre closure, π-closure, and δ-closure) of A and is denoted by rcl(A) (resp. scl(A) cl(A), pcl(A), spcl(A), πcl(A), and δcl(A) ).

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