Continuity on approximation spaces

Abstract

The present paper investigates some of the properties of the induced topology on generalized approximation spaces. The properties of the induced topology are characterized in terms of the type of the binary relation used. Also, the conditions upon which the induced topology will be an indiscrete or a discrete one are derived. Besides, the separation axioms on the induced topological space are studied. Moreover, characterization theorems for continuity of a function and homeomorphism are explored.