Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777793 | Topology and its Applications | 2017 | 11 Pages |
Abstract
In this paper, we consider a common generalization of both hypercontinuous posets and s2-quasicontinuous posets, and introduce a new concept of quasi-hypercontinuous posets. The main results are: (1) A poset is a quasi-hypercontinuous poset iff the upper topology is a hypercontinuous lattice iff the Sâ-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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Xiaoquan Xu, Wenfeng Zhang,