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arXiv · 2611.01545

Idempotent Ultrafilters and Closed Images of Complete Semilattices

Alexander V. Osipov·Konstantin Kazachenko
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Abstract

We prove that every continuous homomorphism from a complete topologized semilattice to a Hausdorff semitopological semilattice has closed image, answering a question of Banakh and Bardyla. The main step is the convergence of idempotent ultrafilters on complete semitopological semilattices. We also prove that, for every complete subsemilattice $X$ of a Hausdorff semitopological semilattice $Y$, the natural order of $X$ is closed in $Y\times Y$. In particular, the natural order of every complete Hausdorff semitopological semilattice $X$ is closed in $X\times X$.

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BibTeXRIS

Alexander V. Osipov, Konstantin Kazachenko. 2026-11-01. Idempotent Ultrafilters and Closed Images of Complete Semilattices. https://arxiv.org/abs/2611.01545

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