Topological Properties in Isotonic Spaces

Abstract

An isotonic space (X, cl) is a set X with isotonic operator cl : P(X) ! P(X) which satisfies cl(;) = ; and cl(A) cl(B) whenever A B X. Many properties which hold in topological spaces hold in isotonic spaces as well. We explore the topological concepts of lower separation axioms, higher separation axioms and connectedness for isotonic spaces, and we establish that they are topological properties in isotonic spaces