Completions of uniform convergence spaces
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- by G. D. Richardson PDF
- Proc. Amer. Math. Soc. 29 (1971), 159-164 Request permission
Abstract:
H. J. Biesterfeldt has shown that a uniform convergence space which satisfies the completion axiom has a completion. In the present paper, we show that every uniform convergence space has a completion. Furthermore, if the uniform convergence space is Hausdorff and satisfies the completion axiom, then it has a Hausdorff completion, which reduces to the Bourbaki completion for uniform spaces. Finally, a uniqueness theorem is obtained.References
- H. J. Biesterfeldt Jr., Completion of a class of uniform convergence spaces, Nederl. Akad. Wetensch. Proc. Ser. A 69=Indag. Math. 28 (1966), 602–604. MR 0205219 N. Bourbaki, General topology, Part I, Hermann, Paris; Addison-Wesley, Reading, Mass., 1966. MR 34 #5044a.
- C. H. Cook and H. R. Fischer, Uniform convergence structures, Math. Ann. 173 (1967), 290–306. MR 217756, DOI 10.1007/BF01781969
- H. R. Fischer, Limesräume, Math. Ann. 137 (1959), 269–303 (German). MR 109339, DOI 10.1007/BF01360965
- G. D. Richardson, A class of uniform convergence structures, Proc. Amer. Math. Soc. 25 (1970), 399–402. MR 256335, DOI 10.1090/S0002-9939-1970-0256335-X
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 159-164
- MSC: Primary 54.30
- DOI: https://doi.org/10.1090/S0002-9939-1971-0282332-5
- MathSciNet review: 0282332