Name
Abstract | ||
|---|---|---|
In a previous paper we constructed a full and faithful functor M from the category of locally compact metric spaces to the category of formal topologies (representations of locales). Here we show that for a real-valued continuous function f,M (f) factors through the localic positive reals if, and only if, f has a uniform positive lower bound on each ball in the locally compact space. We work within the framework of Bishop constructive mathematics, where the latter notion is strictly stronger than point-wise positivity. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1002/malq.200710034 | MATHEMATICAL LOGIC QUARTERLY |
Keywords | Field | DocType |
locales,formal topologies,locally compact metric spaces | Discrete mathematics,Combinatorics,Locally compact space,Locally compact group,Upper and lower bounds,Functor,Uniform continuity,Metric space,Mathematics,Constructive analysis,Mathematical logic | Journal |
Volume | Issue | ISSN |
54 | 1 | 0942-5616 |
Citations | PageRank | References |
2 | 0.71 | 2 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Erik Palmgren | 1 | 233 | 43.17 |