On Singular Sets and Maximal topologies

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 (tau) is non Singular (with respect to P) then every (tau)s- Singular set V U{x} such that x ε CLt V(tau) - Int(tau) *V(tau) is (tau)s open and we provide some theorems.