On Biesterfeldt’s completion axiom spaces
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- by R. J. Gazik
- Proc. Amer. Math. Soc. 52 (1975), 401-405
- DOI: https://doi.org/10.1090/S0002-9939-1975-0375201-7
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Abstract:
It is proved that a Hausdorff, totally bounded Completion Axiom space is a uniform space. The method of proof shows that Hausdorff Completion Axiom spaces have completions (in the embedding sense) which are again Hausdorff Completion Axiom spaces; moreover these completions are uniformly regular, uniformly strict, and have the regular extension property.References
- H. J. Biesterfeldt Jr., Completion of a class of uniform convergence spaces, Indag. Math. 28 (1966), 602–604. Nederl. Akad. Wetensch. Proc. Ser. A 69. MR 0205219, DOI 10.1016/S1385-7258(66)50064-6
- 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
- D. C. Kent and G. D. Richardson, Regular completions of Cauchy spaces, Pacific J. Math. 51 (1974), 483–490. MR 390989, DOI 10.2140/pjm.1974.51.483
- Ellen E. Reed, Completions of uniform convergence spaces, Math. Ann. 194 (1971), 83–108. MR 292021, DOI 10.1007/BF01362537
- 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
- G. D. Richardson, Completions of uniform convergence spaces, Proc. Amer. Math. Soc. 29 (1971), 159–164. MR 282332, DOI 10.1090/S0002-9939-1971-0282332-5
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 401-405
- MSC: Primary 54A20; Secondary 54E15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0375201-7
- MathSciNet review: 0375201