The concepts of pre open sets, semi open sets, ? open sets, ? open sets, and b-open sets introduced by
many authors in topological spaces (cf. [2, 4, 6, 8, 10] ) and extended to bitopological spaces by others
(cf. [9, 11 ] ) . The concept of ?-open sets was introduced and studied by many authors (cf. [ 3,12] ) ,
and extended to bitopological spaces in [ 5] , by defining the concept of ?1 ?2 –generalized ?-closed set.
In this paper many types of weak open sets in bitopological spaces will be defined, Relations
between those sets will be discussed, properties such as supra and infra topological structures will be
determined.
Also a new type of connectedness for bitopological spaces will be defined and preserving that
type of connectedness under certain type of map between bitopological spaces will be proved , many
other results and counter examples ,also will be showed.
Throughout this paper the following notation will be used: ? denotes subset (not necessarily
proper), Ac denotes the complement of A in the space (that A is subset of).
If ( X, ?1, ?2 ) is a bitopological space, A ? X, i-int A and j-cl A denote the interior and closure
of A relative to ?i and ?j respectively , i-open(closed) set denotes ?i open(closed) set (i,j ? {1,2}).