Article ID Journal Published Year Pages File Type
5777793 Topology and its Applications 2017 11 Pages PDF
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 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.
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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