On the use of partial orders in uniform spaces

Bruce S. Burdick


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.


Locally fine; Complete; Supercomplete; Cofinally complete; Paracompact

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Topology and its Applications  vol: 154  issue: 14  first page: 2745  year: 2007  
doi: 10.1016/j.topol.2007.05.008

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

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