A metrizable semitopological semilattice with non-closed partial order [Elektronski vir]
Banakh, Taras, 1968- ; Bardyla, Serhii ; Ravsky, O. V.
We construct a metrizable semitopological semilattice ▫$X$▫ whose partial order ▫$P=\{(x,y)\in X\times X:xy=x\}$▫ is a non-closed dense subset of ▫$X\times X$▫. 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, having a prescribed countable family of convergent sequences.
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