F−open and F−closed sets in Topological Spaces

Abstract

An open (resp., closed) subset A of a topological space (X, T ) is called F-open (resp., F-closed) set if cl(A)\A (resp., A\int(A)) is finite set. In this work, we study the main properties of these definitions and examine the relationships between F-open and F-closed sets with other kinds such as regularly open, regularly closed, closed, and open sets. Then, we establish some operators such as F-interior, F-closure, and F-derived...etc., using F-open and F-closed sets. At the end of this work, we introduce definitions of F-continuous function, F-compact space, and other related properties.