The B-topology on S ∗-doubly quasicontinuous posets

Abstract

Abstract The notions of o s {o}_{s} -convergence and S ∗ {S}^{\ast } -doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence and S ∗ {S}^{\ast } -doubly continuous posets, respectively. We first consider the relationship between o s {o}_{s} -convergence and B-topology and show that the topology induced by o s {o}_{s} -convergence according to the standard topological approach is the B-topology precisely. Then, the topological characterization for the S ∗ {S}^{\ast } -doubly quasicontinuity is presented. It is proved that a poset is S ∗ {S}^{\ast } -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 o s {o}_{s} -convergence being topological is given and the complete regularity of B-topology on S ∗ {S}^{\ast } -doubly quasicontinuous posets is explored.