A metrizable semitopological semilattice with non-closed partial order

Topological Algebra and its Applications

Ravsky Alex¹  Bardyla Serhii²  Banakh Taras³ 

[1] Department of Analysis, Geometry and Topology, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine;Institute of Mathematics, Kurt Gödel Research Center, Vienna, Austria;Ivan Franko National University of Lviv (Ukraine) and Jan Kochanowski University in Kielce,Poland;

关键词: semitopological semilattice;    partial order;    convergent sequence;    act;    semigroup;    54a20;    06a12;    22a26;    37b05;   

DOI  :  10.1515/taa-2020-0006

来源: DOAJ

【 摘 要 】

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, having a prescribed countable family of convergent sequences.

【 授权许可】

Unknown