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Cauchy sequences in semimetric spaces. (English) Zbl 0233.54015


MSC:

54E25 Semimetric spaces
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
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References:

[1] Charles C. Alexander, Semi-developable spaces and quotient images of metric spaces, Pacific J. Math. 37 (1971), 277 – 293. · Zbl 0216.19303
[2] A. Arhangel\(^{\prime}\)skiĭ, Behavior of metrizability in factor mapping, Dokl. Akad. Nauk SSSR 164 (1965), 247 – 250 (Russian).
[3] A. V. Arhangel\(^{\prime}\)skiĭ, Mappings and spaces, Russian Math. Surveys 21 (1966), no. 4, 115 – 162. · Zbl 0171.43603
[4] H. R. Bennett and M. H. Hall, Semi-metric functions and semi-metric spaces, Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970), Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash., 1970, pp. 34 – 38. · Zbl 0197.19302
[5] Morton Brown, Semi-metric spaces, Summer Institute on Set Theoretic Topology, Madison, Wisconsin, Amer. Math. Soc., Providence, R.I., 1955, pp. 62-64.
[6] Robert W. Heath, A regular semi-metric space for which there is no semi-metric under which all spheres are open, Proc. Amer. Math. Soc. 12 (1961), 810 – 811. · Zbl 0116.14303
[7] Ja. A. Kofner, A new class of spaces and some problems from symmetrizability theory., Dokl. Akad. Nauk SSSR 187 (1969), 270 – 273 (Russian). · Zbl 0202.53702
[8] Louis F. McAuley, A relation between perfect separability, completeness, and normality in semi-metric spaces, Pacific J. Math. 6 (1956), 315 – 326. · Zbl 0072.17802
[9] S. I. Nedev, Continuous and semicontinuous \?-metrics, Dokl. Akad. Nauk SSSR 193 (1970), 531 – 534 (Russian). · Zbl 0208.25203
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