A topological space X is called π-normal if for any two disjoint closed subsets A and B of X one of which is π-closed, there exist two open disjoint subsets U and V of X such that A ⊆ U and B ⊆ V. We will present some characterizations of π-normality and some examples to show relations between π-normality and other weaker version of normality such as mild normality, almost normality, and quasi-normality. We investigate in this paper a weaker version of normality called π-normality. We will prove that π-normality is a property which lies between almost normality and normality. We will present some characterizations of π-normality and some examples to show relations between π-normality and other weaker versions of normality such as mild normality, almost normality, and quasi-normality. We will denote an ordered pair by x, y , the set of positive integers by N and the set of real numbers by R. A T 4 space is a T 1 normal space and a Tychonoff space is a T 1 completely regular space. The interior of a set A will be denoted by intA, and the closure of a set A will be denoted by A.
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