Metrically generated theories

Authors:
E. Colebunders and R. Lowen

Journal:
Proc. Amer. Math. Soc. **133** (2005), 1547-1556

MSC (2000):
Primary 54B30, 18B99, 18E20

DOI:
https://doi.org/10.1090/S0002-9939-04-07633-6

Published electronically:
November 19, 2004

MathSciNet review:
2111956

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Abstract | References | Similar Articles | Additional Information

Abstract: Many examples are known of natural functors describing the transition from categories of generalized metric spaces to the ``metrizable" objects in some given topological construct . If preserves initial morphisms and if is initially dense in , then we say that is -metrically generated. Our main theorem proves that is -metrically generated if and only if can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.

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Additional Information

**E. Colebunders**

Affiliation:
Vrije Universiteit Brussel, Vakgroep Wiskunde, Pleinlaan 2, 1050 Brussel, Belgium

Email:
evacoleb@vub.ac.be

**R. Lowen**

Affiliation:
Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020 Antwerp, Belgium

Email:
bob.lowen@ua.ac.be

DOI:
https://doi.org/10.1090/S0002-9939-04-07633-6

Keywords:
Topological construct,
topological space,
metric space,
uniform space,
approach space,
bornological space,
measurable space

Received by editor(s):
September 22, 2003

Received by editor(s) in revised form:
January 5, 2004

Published electronically:
November 19, 2004

Communicated by:
Alan Dow

Article copyright:
© Copyright 2004
American Mathematical Society