384

M . Jelid

DEFINITION 1.4. A bitopological space (Х,тх'^2) ^s pairwise semi То (PSTq) if for each pair {x,y) of distinct points in X re is a set üeso(X,Ti) such>that xeu^ yéu or a set VgS0(X,T2)s^ch that x^, y€v.

DEFINITION 1.5. A bitopological space (Х^т^^тг) is weakly pairwise semi Tq (WPSTq) if for each two distinct points in X re is a set which is either T^-semi open or T2-serai open and tains only one of these points.

DEFINITION 1.6. A bitopological space (X,ti,t2) is strongly pairwise semi Tq (SPSTq) if for every x,yeX, x^^y, there exists a Ti-semi open set U and a T2-semi open set V such that xeu, xgv and y^U, y^V or there exists a T^-semi open set W and a т2-semi open set L such that x^W, x^L and yew, yeL.

DEFINITION 1.7. A bitopological space (X,ti,t2) is weakly irwise semi Tx (WPST^) if for each two distinct points x,yGX re are üeS0(X,Ti) and veS0(X,T2) such that xGU, y^U and yev, x^V.

DEFINITION 1.8. A bitopological space iX,Ti,T2) is pairwise semi Ti (PSTi) if for each pair (x,y) of distinct points of X re are UeS0(X,Ti) and VgS0(X,t2) such that xgU, y^U and yGV, x^V.

PROPOSITION 1.8. A bitopological space (Х,тх,т2) is PSTi iff (X,Ti) is STi space, i=l,2.

The proof follows immediately from the definition of STi and PSTi space.

DEFINITION 1.9. A bitopological space {X,'^i,t^2) is pairwise semi T2 (PST2) if for each pair (x,y) of distinct points of X re exist UGS0(X,Ti) and VGS0(X,t2) such that xGU, yGV and ünv=0.

DEFINITION 1.10. A bitopological space (Х,тх,Т2) is weakly pairwise semi T2(WPST2) if for each two distinct points x,yGX re exist üGS0(X,Ti) and VGS0(X,T2) such that xGU, yGV and unv=0.

For each xgx we introduce the following notations:

bi - scl { x } = T^-scl{x}nT2-scl{x} and bi-sker{x} = т,-sker{x }nT2-sker{x }. A set A is bi-open if AGTj^ and AGT2.