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Abstract: We give a constructive localic account of the completion of quasimetric spaces. In the context of Lawvere's approach, using enriched categories, the points of the completion are flat left modules over the quasimetric space. The completion is a triquotient surjective image of a space of Cauchy sequences and can also be embedded in a continuous dcpo, the "ball domain". Various examples and constructions are given, including the lower, upper and Vietoris powerlocales, which are completions of... (Update)
Cited by: More
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BibTeX entry: (Update)
S.J. Vickers, "Localic Completion of Quasimetric Spaces", in preparation. http://citeseer.ist.psu.edu/vickers97localic.html More
@misc{ vickers-localic,
author = "S. Vickers",
title = "Localic Completion of Quasimetric Spaces",
text = "S.J. Vickers, Localic Completion of Quasimetric Spaces, in preparation.",
url = "citeseer.ist.psu.edu/vickers97localic.html" }
Citations (may not include all citations):126 Cambridge University Press (context) - Johnstone, Spaces - 1982
103 Introduction to Commutative Algebra (context) - Atiyah, MacDonald - 1969
83 Sheaves in Geometry and Logic (context) - Lane, Moerdijk - 1992
83 Topos Theory (context) - Johnstone - 1977
73 Topology via Logic (context) - Vickers - 1989
39 Totally bounded spaces and compact ordered spaces as domains.. (context) - Smyth - 1991
33 A computational model for metric spaces - Edalat, Heckmann
29 and closed categories (context) - Lawvere, spaces et al. - 1973
17 Completeness of quasi-uniform and syntopological spaces (context) - Smyth - 1994
9 Information systems for continuous posets - Vickers - 1993
8 Formal spaces (context) - Fourman, Grayson - 1982
8 Geometric logic in computer science - Vickers
6 Open locales and exponentiation (context) - Johnstone - 1984
6 Topology via constructive logic - Vickers - 1996
6 Locales are not pointless - Vickers
5 Constructive points of powerlocales - Vickers
5 Preframe presentations present - Johnstone, Vickers
3 Topical categories of domains - Vickers - 1997
3 Memoirs of the American Mathematical Society (context) - Joyal, Tierney et al. - 1984
3 Sheaf models for analysis (context) - Fourman, Hyland - 1979
3 Toposes pour les vraiment nuls - Vickers
2 Localic triquotient maps are effective descent maps (context) - Plewe
2 Geometric logic as a specification language - Vickers
1 closed subgroup (context) - Johnstone, constructive - 1989
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Topology via Constructive Logic - Vickers (1999) (Correct)
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