The category of finitary biframes as the category of pointfree bispaces

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 ordered collection quotients (i.e. bispaces). Furthermore, duality bispace associated natural Skula space L. gives us bisobriety weaker than pairwise Hausdorffness, incomparable T1 axiom, stronger T0 axiom. TD introduced, point-set generalization classical It this axiom frame duality.