The assembly of a pointfree bispace and its two variations

We explore a pointfree theory of bitopological spaces (that is, sets equipped with two topologies). In particular, here we regard finitary biframes as duals spaces. particular for biframe $$\mathcal {L}$$ the ordered collection all its bisubspaces (i.e. biquotients) is studied. It shown that this in three meaningful ways. it that, apart from assembly , there are other structures $$\mathsf {A}_{cf}(\mathcal {L})$$ and {A}_{\pm }(\mathcal which both have same main component {A}(\mathcal . The biquotients structure being shows generated by frame patch-closed together patch-fitted ones. positive negative Notions fitness subfitness introduced, analogues characterization theorems these axioms hold. A spatial, version proven, whose spectrum pairwise $$T_1$$ characterized, among things terms {bpt}(\mathsf {L}))$$