On irresolute functions in ideal topological spaces

Abstract

In the ideal topological spaces (X, ?, I) and (Y, J, ?), we define (I, J)-irresolute function, weakly-(I, J)-irresolute, strongly-(I, J)-irresolute functions, semi-I-open sets and quasi-H-closed spaces modulo ideal I. We discuss properties of (I, J)-irresolute function mapping connected, closed, compact ideal spaces modulo I and semi-I-isolated points. (I, J)-Homeomorphisim on presemi-I-open sets and closure properties of quasi-H-closed spaces and semi-I-open subsets are explored in this paper.