The order topology for function lattices and realcompactness
A lattice K(X,Y) of continuous functions on space X is associated to each compactification Y of X. It is shown for K(X,Y) that the order topology is the topology of compact convergence on X if and only if X is realcompact in Y. This result is used to provide a representation of a class of vector lat...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000173 |
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| _version_ | 1832555365090197504 |
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| author | W. A. Feldman J. F. Porter |
| author_facet | W. A. Feldman J. F. Porter |
| author_sort | W. A. Feldman |
| collection | DOAJ |
| description | A lattice K(X,Y) of continuous functions on space X is associated to each compactification Y of X. It is shown for K(X,Y) that the order topology is the topology of compact convergence on X if and only if X is realcompact in Y. This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes every C(X) and all countably universally complete function lattices with 1. It is shown that a choice of K(X,Y) endowed with a natural convergence structure serves as the convergence space completion of V with the relative uniform convergence. |
| format | Article |
| id | doaj-art-e20df8021f2342e796229a07ab7d4ff4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e20df8021f2342e796229a07ab7d4ff42025-02-03T05:48:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014228930410.1155/S0161171281000173The order topology for function lattices and realcompactnessW. A. Feldman0J. F. Porter1Department of Mathematics, University of Arkansas, Fayetteville 72701, AR, USADepartment of Mathematics, University of Arkansas, Fayetteville 72701, AR, USAA lattice K(X,Y) of continuous functions on space X is associated to each compactification Y of X. It is shown for K(X,Y) that the order topology is the topology of compact convergence on X if and only if X is realcompact in Y. This result is used to provide a representation of a class of vector lattices with the order topology as lattices of continuous functions with the topology of compact convergence. This class includes every C(X) and all countably universally complete function lattices with 1. It is shown that a choice of K(X,Y) endowed with a natural convergence structure serves as the convergence space completion of V with the relative uniform convergence.http://dx.doi.org/10.1155/S0161171281000173order topologyrelative uniform convergencerealcompactnessuniversally complete function latticeconvergence space completion. |
| spellingShingle | W. A. Feldman J. F. Porter The order topology for function lattices and realcompactness International Journal of Mathematics and Mathematical Sciences order topology relative uniform convergence realcompactness universally complete function lattice convergence space completion. |
| title | The order topology for function lattices and realcompactness |
| title_full | The order topology for function lattices and realcompactness |
| title_fullStr | The order topology for function lattices and realcompactness |
| title_full_unstemmed | The order topology for function lattices and realcompactness |
| title_short | The order topology for function lattices and realcompactness |
| title_sort | order topology for function lattices and realcompactness |
| topic | order topology relative uniform convergence realcompactness universally complete function lattice convergence space completion. |
| url | http://dx.doi.org/10.1155/S0161171281000173 |
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