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A note on sequentially compact quasi-pseudo-metric spaces

Abstract

It is asked in [3] whether sequential compactness is equivalent to compactness in a quasi-pseudo-metric space. In this note we give a counterexample and a proposition relating to this question.

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References

  1. [1]

    Künzi, H. P. A.: Quasi-metrisierbare Räume. Dissertation. Universität Bern. 1981.

  2. [2]

    Niemytzki, V.: Über die Axiome des metrischen Raumes. Math. Ann.104, 666–671 (1931).

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  3. [3]

    Reilly, I. L., Subrahmanyam, P. V., Vamanamurthy, M. K.: Cauchy sequences in quasi-pseudo-metric spaces. Mh. Math.93, 127–140 (1982).

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Künzi, H.P.A. A note on sequentially compact quasi-pseudo-metric spaces. Monatshefte für Mathematik 95, 219–220 (1983). https://doi.org/10.1007/BF01351999

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Keywords

  • Sequential Compactness