On Singular Sets and Maximal topologies

Abstract

In this Work , we study The concept of maximal topologies and its relation with Singular sets , furthermore we study the spaces which are maximal with respect to semi- regular property and we proved that if t is sub maximal has property P then τ is maximal P if and only if τ is non singular (with respect to P) we prove that if P is contractive, semi – regular and t is non Singular (with respect to P) then every ts- Singular set V {x} such that x Î is ts-open and we provide some theorems.