The sigma(1)-topology and lambda(1)-topology on s(1)-quasicontinuous posets

摘要

In this paper, we consider a common generalization of both s(1)-continuous posets and quasicontinuous domains, and we introduce new concepts of way below relations and s(1)-quasicontinuous posets. The main results are: (1) A poset is an s(1)-quasicontinuous poset iff the sigma(1)-topology is a hypercontinuous lattice iff the s*-convergence is topological with respect to the sigma(1)-topology; (2) A poset is s(1)-continuous iff it is meet s(1)-continuous and s(1)-quasicontinuous; (3) The Ai-topology on an lambda(1)-quasicontinuous poset is Tychonoff; (4) A poset P is s(1)-quasicontinuous and the sigma(1)-topology is sober iff P is a quasicontinuous domain and the sigma(1)-topology coincides with the Scott topology. (C) 2016 Elsevier B.V. All rights reserved.