On RG-spaces and the regularity degree
We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2006-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1934 |
| Summary: | We continue the study of a lattice-ordered ring G(X), associated with the ring C(X). Following, X is called RG when G(X) = C(Xδ). An RG-space must have a dense set of very weak P-points. It must have a dense set of almost-P-points if Xδ is Lindelöf, or if the continuum hypothesis holds and C(X) has small cardinality. Spaces which are RG must have finite Krull dimension when taken with respect to the prime z-ideals of C(X). There is a notion of regularity degree defined via the functions in G(X). Pseudocompact spaces and metric spaces of finite regularity degree are characterized. |
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| ISSN: | 1576-9402 1989-4147 |