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Feebly pT(i,k)-spaces in bitopological spaces
Zahir Dobeas AL- NafieBabylon University2006
Abstract
In this research we studied a PT(i,k)-spaces by using feebly sets which defined by maheshwari and we find a relation between these spaces and we called it a feebly PT(i,k)-spaces.
In this research we studied a PT(i,k)-spaces by using feebly sets which defined by maheshwari and we find a relation between these spaces and we called it a feebly PT(i,k)-spaces.
Introduction
S.N Maheshwari (1990) define a feebly open set in a topological space . A set A is said to be feebly open (Gyn and Lee ,1984) if there exist an open set O in X such that O?A?scl(O) where scl denotes the closure set in the topological space .
In bitopological space (X,T1,T2) M. Jelic (1994) give a new definition of pair wise T(i,k))-spaces . A bitopological space X is said to be a pair wise T(i,k) –space if for every x?X and every pTk-open cover U of X there exist a pTi –open V of X and a u?U such that st(x,v)?U , i,k?{1,2,3} ,and it is denoted by pT(i, k)-space .In this paper we shall introduce a new definition of pT(i, k)-space by using feebly open set and we shall investigate the relation between these spaces .
preliminaries
In this section we shall investigate some properties of feebly open sets in bitopological spaces and give a new definition of pTi-cover by using a feebly open set and discuss a relation between them.
Remark(2-1) (Gyn and Lee ,1984) Every open set is feebly –open set and the converse is not true.
Theorem (2-2) (Gyn and Lee ,1984) Any union of feebly –open sets is feebly open.
Definition(2-3) (Gyn and Lee ,1984) A point p in X is said to be feebly interior point of A if A is feebly neighborhood of p , and the set of all feebly interior points of A is denoted by int(A)
Definition(2-4) (Gyn and Lee ,1984) A set A in a topological space is said to be feebly–closed if it is complement is feebly open.
Remark(2-5) S.N Maheshwari (1990) A set A in a topological space is feebly–open iff fint(A)= A
Remark(2-6) (Gyn and Lee ,1984)
- وصف الــ Tags لهذا الموضوع
- bitopological , spartion axioms
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