On a weak form separation axioms and continuous functions in ?- bitopological spaces Zahir D. AL- Nafie and Ameer A. J. AL –Swidi University of Babylon ,Collage of Education Ibn- Hayaan ,Math. Departement. Abstract The aim of this paper is to introduced a new types of separation axioms in bitopological spaces which is defined by an ?- open set which is defined by H.Z .Hdeib[3] in 1982 ,many results and relation ships are studied in this paper Key words: ?- open set, pre-open set ,? –open set ,separation axioms , bitopological space. Introduction: 1. A bitopological space is a non – empty set X with two topologies ?1, ?2 defined on it or it is the triple( X, ?1, ?2) ,such that ( X, ?1),(X, ?2) are two topological spaces defined on X ,AL- Swidi and Asaad M .A.Alhosaini [1 ] , introduced a new notions on an ij- ?- open set in bitopological spaces in 2011 The concept of pre open sets ,semi open sets, ? open sets,? open sets ,and b open sets were introduced by ( cf. [ 2,4,6,7 ] ) and extended by (cf. [ 9,10 ]). Let (X ,? ) be a topological space , A X , a point x X ,is called a condensation point if for each U ? with x U ,the set U A is uncountable . A is said to be an ?-closed if it contains all its condensation points ,the complement of ?-closed is said to be ?-open set .equivalently a set W is ?-open if for each x W ,there exist U ? with x U and U-W is countable[3]. The family of all ?-open set in(X ,? ) , denoted by ,forms a topology on X finner than ?.the ?-closure and ?-interior of a set A will be denoted by cl A and int A resp. , are defined by: cl A= {F X/F is ?-closed and A F} int A= { G X/G is ?-open and G A} In 2009 [10]T.Noiri ,A, AL- Omari ,M,S,M. Lorain introduced and discussed a new notions called( ?-?-open, pre-? –open ,and b-? –open) sets in topological spaces.