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On pair wise a-continuous and pair wise pre continuous mappings
zahir dobeas al-nfie
department of math.college of education ,
Babylon university
abstract
[A.S.mashhour , I.A.hasanein and S.N.el-deeb] in 1983 studied sevsral of a-continuous and a-open mapping in topological spaces in this search we show that results similar th these in bitopolopological spaces.
Introduction
Let X,Y,Z be topological spaces on which no separation axioms are assumed unless explicitly stated , let S be a subset of X , the closure (resp. interior ) of S will be denoted by cl(s) (resp. int(S)) . a subset of S of X is called a-set [5] (resp. semi-open set[3] , pre open set [4]) if S?int(cl(int(S)) (resp. S?cl(int(S)) , S?int(cl(S))) , the complement of an a-set (resp. semi-open set, preopen set) is called a-closed (resp. semi-closed , pre closed ) the space of all a-set(semi-open ,pre open ) is denoted a(X)(resp. SO(X),PO(X)) .it is clear that each a-set is semi-open and pre open and the converse is not true.
A mapping f:X®Y is called almost continuous [7] if for each xIX and each open neighborhood V of f(x) there exist an open neighborhood U of x such that f(U)?int(cl(V)) , and it is called q-continuous if f(U)?cl(V) , a mapping f:X®Y is called seif the inverse image of each open set in Y is mi-open set in X and f is called a-continuous if the inverse image of each open set is an a-open set in X [2], and if it is called a-open if the image of each open set is a-open set Y.
- وصف الــ Tags لهذا الموضوع
- ?-continuous,?-open
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