Topology is a beautiful science and forms a bridge between geometry and algebra.Topology means (Topo-place,logy-study) i.e.,study of place.One of the most wiedly used mathematical concepts in the study of place,optimization of any machinery parts such as mobiles,cycles,computers,cars,buses,trains and airplanes,etc.In this paper,the concept of a separation axioms considered.The separation axioms are only in the sense that when defining the notation of topological space.The separation axims are denoted with the letter “T” after the German Trennungsaxiom,which means “Separation Axioms”.In this paper proposed T0,T1,T2,T3 and T4 axioms with examples