On the use of partial orders in uniform spaces
We investigate the use of nets indexed by preorders in uniform spaces. Nine different Cauchy conditions and four different convergence conditions yield 36 completeness properties, each of which turns out to be equivalent to a known form of completeness. We also use these preordered nets to character...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2003-04-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/2013 |
| Summary: | We investigate the use of nets indexed by preorders in uniform spaces. Nine different Cauchy conditions and four different convergence conditions yield 36 completeness properties, each of which turns out to be equivalent to a known form of completeness. We also use these preordered nets to characterize the functors θ, λ, and v, which are associated with these completeness properties. In the case of λ we give an example to show that the analogous characterization with predirected nets does not work. |
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| ISSN: | 1576-9402 1989-4147 |