Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit
The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmat...
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2018-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | http://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdf |
| _version_ | 1818268588094521344 |
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| author | Bernhard Banaschewski Anthony W. Hager |
| author_facet | Bernhard Banaschewski Anthony W. Hager |
| author_sort | Bernhard Banaschewski |
| collection | DOAJ |
| description | The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), 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 $C(T)$. |
| first_indexed | 2024-12-12T20:40:52Z |
| format | Article |
| id | doaj.art-72a47212381c431e8abdd2b0c149fe49 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-12T20:40:52Z |
| publishDate | 2018-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-72a47212381c431e8abdd2b0c149fe492022-12-22T00:12:45ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612018-07-019111361475Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unitBernhard Banaschewski0Anthony W. Hager1Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario L85 4K1, Canada.Department of Mathematics and CS, Wesleyan University, Middletown, CT 06459.The category of the title is called $mathcal{W}$. This has all free objects $F(I)$ ($I$ a set). For an object class $mathcal{A}$, $Hmathcal{A}$ consists of all homomorphic images of $mathcal{A}$-objects. This note continues the study of the $H$-closed monoreflections $(mathcal{R}, r)$ (meaning $Hmathcal{R} = mathcal{R}$), 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 $C(T)$.http://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdfArchimedean $ell$-group$H$-closed monoreflectionYosida representationcountable compositionepicompleteBaire functions |
| spellingShingle | Bernhard Banaschewski Anthony W. Hager Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit Categories and General Algebraic Structures with Applications Archimedean $ell$-group $H$-closed monoreflection Yosida representation countable composition epicomplete Baire functions |
| title | Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit |
| title_full | Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit |
| title_fullStr | Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit |
| title_full_unstemmed | Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit |
| title_short | Representation of $H$-closed monoreflections in archimedean $ell$-groups with weak unit |
| title_sort | representation of h closed monoreflections in archimedean ell groups with weak unit |
| topic | Archimedean $ell$-group $H$-closed monoreflection Yosida representation countable composition epicomplete Baire functions |
| url | http://cgasa.sbu.ac.ir/article_61475_f777dd362fb1959c3a9aa5115a63f9a9.pdf |
| work_keys_str_mv | AT bernhardbanaschewski representationofhclosedmonoreflectionsinarchimedeanellgroupswithweakunit AT anthonywhager representationofhclosedmonoreflectionsinarchimedeanellgroupswithweakunit |