Closures and topological closures in quasi-discrete closure spaces

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 clcl and its topological closure clTclT are respectively generated by relations RR and SS, then SS is the transitive closure of RR.