부산대학교 도서관

The notion of a pairwise $\alpha$-open subset of a bitopological space and 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 in bitopological space. They establish the relationship of the introduced notion 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. An equivalent relation between these spaces is established. It is shown that this property is hereditary on $X$. The arbitrary union of pairwise $\alpha$-$I$-open sets is open, whereas the intersection of two pairwise $\alpha$-$I$-open sets is not necessarily pairwise $\alpha$-$I$-open. The authors also define pairwise $\alpha$-$I$-closed sets and the pairwise $\alpha$-$I$-closure of a set. The notion of a pairwise $\alpha$-$I$-continuous function and an $\alpha$-$I$-irresolute function is introduced and their different properties are studied.