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arXiv · 1902.08760

A metrizable semitopological semilattice with non-closed partial order

Taras Banakh·Serhii Bardyla·Alex Ravsky
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Abstract

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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Taras Banakh, Serhii Bardyla, Alex Ravsky. 2019-02-23. A metrizable semitopological semilattice with non-closed partial order. https://doi.org/10.15673/tmgc.v13i3.1756

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