The concepts of regular open , regular closed , semiopen , semiclosed , and preopen
sets have been introduced by many authors in a topological space ( cf. [ 1-4] ). These
concepts are extended to bitopological spaces by many authors ( cf. [5-7]) .
Throughout the present paper ( X , 1 2 ? ,? ) and ( Y, 1 2 ? ,? ) ( or simple X and Y )
denote bitopological spaces . when A is a subset of a space X , we shall denote the
closure of A and the interior of A in ( X , i ? ) by i ? -clA and i ? -intA , respectively,
where i= 1,2 , and i,j = 1,2 ; i ? j .
A subset A of X is said to be ij- preopen ( resp. ij-semiopen ,ij-regular open ,
ij-regular closed and ij-preclosed ) if
A int( clA) ( resp. A cl( int A), i j i j ?? ? ? ? ?? ? ? ? A int( clA) i j ?? ? ? ? ,
A cl( int A), j i ?? ? ? ? and cl( int A) A ) j i ? ? ? ? ? . The family of all ij-semiopen (
resp. ij- regular open and ij- preopen ) sets of X is denoted by ij-SO(X) ( resp. ij-
RO(X) and ij-PO(X) ) . The intersection of all ij- preclosed sets which contain A is
called the ij- preclosure of A and is denoted by ij-PclA . Obviously , ij-PclA is the
smallest ij-preclosed set which contains