CHARACTERIZATION OF SOME BITOPOLOGICAL PROPERTIES VIA PAIRWISE SETS I. DOCHVIRI Abstract. In the present paper, the classes of pairwise open and pairwise closed sets for bitopological spaces are introduced. Con- ditions by which the almost Baire bitopological property holds are established. Theorems on congruence of two continuous mappings, on inclusion of the image of the complement of a dense set in the complement of its image, and on the continuity of weakly continuous mappings, are proved. Also some results on the intermediate compact set in locally compact bitopological spaces and on the separation of two closed sets in a doubly-finally compact space are obtained. 1. Introduction Intensive study of asymmetric topology is connected with the appearance of the works by [?, ?, 8] [10], and [11]. One of the central concepts in asym- metric topology is the notion of a bitopological space. A bitopological space is a triple (X, τ 1 ,τ 2 ), where τ 1 and τ 2 are independent, generally speaking, topologies on the set X [?, 8] The basic problem of the theory of bitopo- logical spaces is to investigate mathematical objects depending mainly on the topologies τ 1 and τ 2 simultaneously. Bitopological methods allow one to characterize a large number of objects which involuntarily were found beyond the framework of the classical (symmetric) topology. Relying on general topological constructions, there naturally arises desire to generalize topological facts to bitopological ones which frequently lead to a discovery of new important properties of bitopological spaces. Contribution to the rise of bitopological problems, besides a purely topological nature, make the problems connected with asymmetric objects in some other areas of modern mathematics (see, for e.g., [?, ?, 4] [?, 7]. In the present work we introduce the classes of pairwise (briefly p-) open and p-closed sets which are used when establishing some properties of bitopological spaces and their mappings. Throughout the paper, use will be made of the bitopological notions given in [?, 4]nd the designations which will be given below. When we speak on topological spaces we use the no- tations from [?, 5] As usual, by τ i int A and τ j clA, where i, j ∈{1; 2}, we 1991 Mathematics Subject Classification. 54E55. Key words and phrases. Bitopological space, pairwise open and pairwise closed sets, almost (i, j )-Baire space, (i, j )-locally compact space, finally compact space. 1