부산대학교 도서관

The notion of a pairwise $\alpha$-open subset of a bitopological spaceand a pairwise $\alpha$-continuous function was introduced by M.Jelić [Rend. Circ. Mat. Palermo (2) Suppl. No. 24 (1990),387--395; MR1108222]. The notion of an$\alpha$-$I$-open subset of a topological space was introduced by E.Hatır and T. Noiri [Acta Math. Hungar. {\bf 96} (2002), no.~4,341--349; MR1922679]. Motivated by these two articles,the authors introduce the notion of pairwise $\alpha$-$I$-open sets inbitopological space. They establish the relationship of the introducednotion with the pairwise $I$-open set, the pairwise pre-$I$-open set,the pairwise $b$-$I$-open set and the pairwise $\beta$-$I$-open set. Anequivalent relation between these spaces is established. It is shownthat this property is hereditary on $X$. The arbitrary union ofpairwise $\alpha$-$I$-open sets is open, whereas the intersection oftwo pairwise $\alpha$-$I$-open sets is not necessarily pairwise$\alpha$-$I$-open. The authors also define pairwise $\alpha$-$I$-closedsets and the pairwise $\alpha$-$I$-closure of a set. The notion of apairwise $\alpha$-$I$-continuous function and an$\alpha$-$I$-irresolute function is introduced and their differentproperties are studied.