Topological Properties like Separation Axioms Satisfying Properly Hereditary Property

In this paper we shall improve the definition of "properly hereditary property" which raised previously [1] and we shall prove that the topological properties: Functionally Hausdorff, T1 2/3, completely regular, normal, perfectly normal, S2, S∞, locally connected, locally strongly connected, totally disconnected and Riesz separation axiom: TR are properly hereditary properties.