On Singular Sets and Maximal topologies

Abstract

Abstract: In this research, we studied the maximal topologies and their relationship to individual groups. In addition, we studied the maximal spaces dependent on the semi-regular property and proved that if  is a partial maximum that has the property P, then  is the greatest P if and only if  is not singular (depending on the property P), and we prove if  is P is semi-regular,  is not singular (depending on the property P), each group is singular - s and V {x}, so that x is open - s and we proved some other theorems.