The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

In this paper, we first define soft u-open sets and s-open as two new classes of on bitopological spaces. We show that the class p-open lies strictly between these classes, give several sufficient conditions for equivalence each sets, respectively. addition to these, introduce u-?-open, p-?-open, s-?-open three in spaces, which contain Via notions Lindelöfeness SBTSs. discuss relationship notio...

In Domain Theory quasicontinuous domains pop up from time to time generalizing slightly the powerful notion of a continuous domain. It is the aim of this paper to show that quasicontinuous domains occur in a natural way in relation to the powerdomains of finitely generated and compact saturated subsets. Properties of quasicontinuous domains seem to be best understood from that point of view. Th...

Sobriety is a subtle notion of completeness for topological spaces: A space is sober if it may be reconstructed from the lattice of its open subsets. The usual criterion to check sobriety involves either irreducible closed subsets or completely prime lters of open sets. This paper provides an alternative possibility, thus trying to make sobriety easier to understand. We deene the notion of obse...