The upper topology and interval topology on quasi-hypercontinuous posets

摘要

In this paper, we consider a common generalization of both hypercontinuous posets and s(2)-quasicontinuous posets, and introduce a new concept of quasi-hypercontinuous posets. The main results are: (1) A poset is a quasi-hypercontinuous poset if the upper topology is a hypercontinuous lattice iff the S*-convergence is topological with respect to the upper topology; (2) For a quasi-hypercontinuous poset, the quasi-liminf convergence is topological with respect to the interval topology; (3) The interval topology on a quasi-hypercontinuous poset is Tychonoff; (4) A lattice is quasi-hypercontinuous as a poset iff its normal completion is a quasi-hypercontinuous lattice. (C) 2017 Published by Elsevier B.V.