Some minimum topological spaces, and vector lattices
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909986535243776 |
|---|---|
| author | Carrera, R. E. Hager, A. W. Wynne, B. |
| author_facet | Carrera, R. E. Hager, A. W. Wynne, B. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06310 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some minimum topological spaces, and vector lattices Carrera, R. E. Hager, A. W. Wynne, B. Functional Analysis General Topology 54D80, 06F20, 54C10, 08C05 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). |
| title | Some minimum topological spaces, and vector lattices |
| topic | Functional Analysis General Topology 54D80, 06F20, 54C10, 08C05 |
| url | https://arxiv.org/abs/2601.06310 |