Topological properties defined in terms of generalized open sets

Abstract

This paper covers some recent progress in the study of sg-open sets, sg-compact spaces, N-scattered spaces and some related concepts. A subset $A$ of a topological space $(X,\tau)$ is called sg-closed if the semi-closure of $A$ is included in every semi-open superset of $A$. Complements of sg-closed sets are called sg-open. A topological space $(X,\tau)$ is called sg-compact if every cover of $X$ by sg-open sets has a finite subcover. N-scattered space is a topological spaces in which every nowhere dense subset is scattered.