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arXiv · 2601.06310

Some minimum topological spaces, and vector lattices

R. E. Carrera·A. W. Hager·B. Wynne
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Abstract

We investigate the existence of compact Hausdorff spaces $X$ that are minimum with respect to $cX=K$ for some fixed covering operator $c$ and compact Hausdorff space $K$ with $cK=K$. Then, using the Yosida representation theorem, we show how that situation relates to the existence of Archimedean vector lattices $A$ with distinguished strong unit that are minimum with respect to $hA=H$ for some fixed hull operator $h$ and vector lattice $H$ with $hH=H$. Among others, we obtain answers for $c=g$ (the Gleason covering operator), $c=qF$ (the quasi-$F$ covering operator), $h = u$ (the uniform completion operator), and $h=e$ (the essential completion operator).

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R. E. Carrera, A. W. Hager, B. Wynne. 2026-01-09. Some minimum topological spaces, and vector lattices. https://arxiv.org/abs/2601.06310

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