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Notes On Weakly Separation Properties | ||
| journal of the college of basic education | ||
| Article 1, Volume 11, Issue 53, 2008, Pages 27-32 | ||
| Author | ||
| Khalid Ali Hussein Al-Mustansiriyah University College of Education | ||
| Abstract | ||
| Notes On Weakly Separation Properties ABSTRACT In this work , we obtain the definitions to - and - , also we study the relationship between - , - , - and - , and give the relation between them and the ordinary separation axioms with examples . 1-Introduction 1-1 Definition : Let (X,T) be¬ a topological space and A X , A is called α – open set in X if and only if A . the fa¬¬¬¬mily of all α –set in X denoted by ; ={ A : A X ; A } where (o) is interior and (-) is closure . [3] 1-2 Definition :1- A space X is called a space ,if for every finite subset F of X, and every y F, there exist a set A containing F and disjoint from y , such that A either open or closed .[1]2- A space X is called a space , if for every singleton set in X is either open or closed .[1]1-3 Example : Let X = {a,b} , T = { X, , {a} } , then = { X, , {a} } , this space its called a Seprenki space, and its clear is a , also (X, ) its . 1-4 Definition : Let (X,T) be¬ a topological space ,and A X , then A is called α –closed set in X iff (X – A) is α – open set. [3] | ||
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