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Cauchy Completion Categories

Published online by Cambridge University Press:  20 November 2018

D. C. Kent  and
G. D. Richardson
D. C. Kent
Affiliation:
Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164
G. D. Richardson
Affiliation:
Departments of Mathematics and Statistics, University of Central Florida, Orlando, FL 32816
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Abstract

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A general procedure is introduced for identifying categories of Cauchy spaces which have completions which possess a certain convergence property P, and for constructing completion functors on such categories. These results are applied to obtain a characterization of Cauchy spaces which allow T3 completions, and to construct T3 completions for categories of Cauchy groups and Cauchy lattices.

Keywords

54A2054E1528A35Cauchy spaceCauchy groupCauchy latticecompletion functorCauchy category
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 1 , 01 March 1989 , pp. 78 - 84
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Ball, R., Convergence and Cauchy Structures on Lattice Ordered Groups, Trans. Amer. Math. Soc. 259 (1980), 357–392.Google Scholar
2. , Distributive Cauchy Lattices, Algebra Universalis 18 (1984), 134–174. Google Scholar
3. Fric, R. and D. C. Kent, Completion Functors for Cauchy Spaces, Internat. J. Math. & Math. Sci. 2 (1979), 589–604. Google Scholar
4. , A Completion Functor for Cauchy Groups, Internat. J. Math. & Math. Sci. 4 (1981), 55–65. Google Scholar
5. Keller, H. H., Die Limes-Uniformisierbarkeit der Limesraume, Math. Ann. 176 (1968), 334-341Google Scholar
6. Kent, D. C., Completions of l-Cauchy Groups, Ordered Groups, Marcel Dekker, Inc., New York and Basel (1980), 93–97.Google Scholar
7. , The Regularity Series of a Cauchy Space, Internat. J. Math. & Math. Sci. 7 (1984), 1–13. Google Scholar
8. Kent, D. C. and Richardson, G. D., Cauchy Spaces with Regular Completions, Pacific J. Math. III (1984), 105–116.Google Scholar
9. Reed, E. E., Completions of Uniform Convergence Spaces, Math. Ann. 194 (1971), 83–108.Google Scholar
10. Wyler, O., Ein Komplettierungsfunktor fur Uniforme Limesrâume, Math. Nachr. 46 (1970), 1–12. Google Scholar