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arXiv · 1806.02864

On images of complete topologized subsemilattices in sequential semitopological semilattices

Taras Banakh·Serhii Bardyla
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Abstract

A topologized semilattice $X$ is called complete if each non-empty chain $C\subset X$ has $\inf C\in\bar C$ and $\sup C\in\bar C$. We prove that for any continuous homomorphism $h:X\to Y$ from a complete topologized semilattice $X$ to a sequential Hausdorff semitopological semilattice $Y$ the image $h(X)$ is closed in $Y$.

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Taras Banakh, Serhii Bardyla. 2018-06-07. On images of complete topologized subsemilattices in sequential semitopological semilattices. https://doi.org/10.1007/s00233-019-10061-w

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