A metrizable semitopological semilattice with non-closed partial order
We construct a metrizable semitopological semilattice X whose partial order P = {(x, y) ∈ X × X : xy = x} is a non-closed dense subset of X × X. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) Hausdorff topology on a set, act, semigroup or semilattice,...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-04-01
|
| Series: | Topological Algebra and its Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/taa-2020-0006 |