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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171281000173 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |