We introduce a new class of sets namely \((1, 2)^\star\)-\(\check{g}_\alpha\)-closed sets, 2)^\star\)-\(\Lambda_{\mathcal{G}}\)-set, 2)^\star\)-\(\lambda_{\mathcal{G}}\)-set and 2)^\star\)-\(\check{g}_\alpha\)-Locally closed are study in bitopological spaces. prove that this classes lies between 2)^\star\)-\(\alpha\)-closed 2)^\star\)-\(\alpha g\)-closed sets. Furthermore, we discuss some essen...

We consider the C*-algebraRq generated by the representation of the q-commutation relations on the twisted Fock space. We construct a canonical unitary U (= U(q)) from the twisted Fock space to the usual Fock space, such that URqU∗ contains the extended Cuntz algebra R0, for all q ∈ (−1, 1). We prove the equality URqU∗ = R0 for q satisfying: q < 1− 2|q|+ 2|q| − 2|q| + · · ·+ 2(−1)k|q|k2 + · · ·...

Based on the theory of frames we introduce a Stone duality for bitopological spaces. The central concept is that of a d-frame, which axiomatises the two open set lattices. Exploring the resulting concept of d-sobriety we find this to be a much more inclusive concept than usual sobriety. Spatial d-frames suggest additional axioms that lead us to define reasonable d-frames; these have an alternat...