The B-topology on S∗-doubly quasicontinuous posets

Abstract

The notions of os{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 os{o}_{s}-convergence and B-topology and show that the topology induced by os{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 os{o}_{s}-convergence being topological is given and the complete regularity of B-topology on S∗{S}^{\ast }-doubly quasicontinuous posets is explored.

Keywords

• os-convergence
• b-topology
• s∗-doubly quasicontinuous poset
• 54a20
• 06a06