Closures and topological closures in quasi-discrete closure spaces

Abstract

Closure space was introduced by Cech as a generalization of ordinary topology. In this work we establish a one to one correspondence between quasi-discrete closures and reflexive relations. We show that, in a quasi-discrete closure space, if a closure c l and its topological closure c l T are respectively generated by relations R and S , then S is the transitive closure of R .