Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658099 | Topology and its Applications | 2016 | 7 Pages |
Abstract
In this note it is proved that for a quasicontinuous lattice L , the lower topology ω(L)ω(L) and the Scott topology σ(L)σ(L) are duals for each other; and if L is a complete lattice such that σ(L)σ(L) is continuous but not hypercontinuous (equivalently, L is not quasicontinuous), then ω(L)ω(L) is not the dual of σ(L)σ(L) and hence they are not duals for each other.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Xiaoquan Xu,