On Quasi B-Open Functions and Quasi B-Closed Functions (Report‪)‬

[section]1. Introduction and preliminaries Functions and of course open functions stand among the most important notions in the whole of mathematical science. Many different forms of open functions have been introduced over the years. Various interesting problems arise when one considers openness. Its importance is significant in various areas of mathematics and related sciences. Since 1996, when Andrijevic [1] has introduced a weak form of open sets called b-open sets. In the same year, this notion was also called sp-open sets in the sense of Dontchev and Przemski [2] but one year later are called [gamma]-open sets due to El-Atik [5]. In this paper, we will continue the study of related functions by involving b-open sets. We introduce and characterize the concept of quasi-b-open functions and quasi-b-closed functions in topological space. Throughout this paper, spaces means topological spaces on which no separation axioms are assumed unless otherwise mentioned and f : (X, [tau]) [right arrow] (Y, [sigma]) (or simply f : X [right arrow] Y) denotes a function f of a space (X, [tau]) into a space (Y, [sigma]). Let A be a subset of a space X. The closure and the interior of A are denoted by Cl(A) and Int(A), respectively. A subset A of a space (X, [tau]) is called b-open [1] (= sp-open [2], [gamma]-open [5]) if A [subset] Cl(Int(A)) [union] Int(Cl(A)). The complement of a b-open set is called b-closed. The union (resp. intersection) of all b-open (resp. b-closed) sets, each contained in (resp. containing) a set A in a space X is called the b-interior (resp. b-closure) of A and is denoted by b-Int(A) (resp. b-Cl(A)) [1].