Some Properties of Semi ${}^{\#}$ Generalized Open Sets in Topological Spaces

Abstract

In this paper a new class of generalized open sets in topological spaces, namely semi ${}^{\#}$ generalized open(briefly, $s^{\#}$g-open) sets is introduced. We prove that this class lies between the class of sg-open sets and the class of gs-open sets and we study some basic properties and characterizations of $s^{\#}$g-open sets. Also we introduce $s^{\#}$g-neighbourhood (shortly, $s^{\#}$-neighbourhood), $s^{\#}$g-interior, $s^{\#}$g-closure and $s^{\#}$g-derived set of a set in a topological spaces and investigate some basic properties of these sets.