The B-topology on S∗-doubly quasicontinuous posets - Sun Tao (De Gruyter, 2021)
The notions of oso_{s}-convergence and S∗S^{* }-doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence and S∗S^{* }-doubly continuous posets, respectively. We first consider the relationship between oso_{s}-convergence and B-topology and show that the topology induced by oso_{s}-convergence according to the standard topological approach is the B-topology precisely. Then, the topological characterization for the S∗S^{* }-doubly quasicontinuity is presented. It is proved that a poset is S∗S^{* }-doubly quasicontinuous iff the poset equipped with the B-topology is locally hyperclosed iff the lattice of all B-open subsets of the poset is hypercontinuous. Finally, the order theoretical condition for the oso_{s}-convergence being topological is given and the complete regularity of B-topology on S∗S^{* }-doubly quasicontinuous posets is explored.