On Semi-Continuous and Clisquish Functions in Generalized Topological Spaces

Abstract

In this paper, we will focus on three types of functions in a generalized topological space, namely; lower and upper semi-continuous functions, and cliquish functions. We give some results for nowhere dense sets and for second category sets. Further, we discuss the nature of cliquish functions in generalized metric spaces and provide the characterization theorem for cliquish functions in terms of nowhere dense sets.

Keywords

• Baire space
• nowhere dense
• lower semi-continuous function
• upper semi-continuous function
• cliquish function