@article {
author = {Banaschewski, Bernhard and Hager, Anthony W.},
title = {Representation of $H$-closed monoreflections in archimedean $\ell$-groups with weak unit},
journal = {Categories and General Algebraic Structures with Applications},
volume = {9},
number = {1},
pages = {1-13},
year = {2018},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.9.1.1},
abstract = { The category of the title is called $\mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $\mathcal{A}$, $H\mathcal{A}$ consists of all homomorphic images of $\mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(\mathcal{R}, r)$ (meaning $H\mathcal{R} = \mathcal{R}$), about which we show ({\em inter alia}): $A \in \mathcal{A}$ if and only if $A$ is a countably up-directed union from $H\{rF(\omega)\}$. The meaning of this is then analyzed for two important cases: the maximum essential monoreflection $r = c^{3}$, where $c^{3}F(\omega) = C(\RR^{\omega})$, and $C \in H\{c(\RR^{\omega})\}$ means $C = C(T)$, for $T$ a closed subspace of $\RR^{\omega}$; the epicomplete, and maximum, monoreflection, $r = \beta$, where $\beta F(\omega) = B(\RR^{\omega})$, the Baire functions, and $E \in H\{B(\RR^{\omega})\}$ means $E$ is {\em an} epicompletion (not ``the'') of such a $C(T)$.},
keywords = {Archimedean $ell$-group,$H$-closed monoreflection,Yosida representation,countable composition,epicomplete,Baire functions},
url = {https://cgasa.sbu.ac.ir/article_61475.html},
eprint = {https://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdf}
}