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Cauchy sequences in quasi-pseudo-metric spaces

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Abstract

This paper considers the problem of defining Cauchy sequence and completeness in quasi-pseudo-metric spaces. The definitions proposed allow versions of such classical theorems as the Baire Category Theorem, the Contraction Principle and Cantor's characterization of completeness to be formulated in the quasi-pseudo-metric setting.

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Authors and Affiliations

  1. Mathematics Department, University of Auckland, Auckland, New Zealand

    I. L. Reilly & M. K. Vamanamurthy

  2. School of Mathematics, University of Hyderabad, Hyderabad, India

    P. V. Subrahmanyam

Authors
  1. I. L. Reilly
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  2. P. V. Subrahmanyam
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  3. M. K. Vamanamurthy
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Reilly, I.L., Subrahmanyam, P.V. & Vamanamurthy, M.K. Cauchy sequences in quasi-pseudo-metric spaces. Monatshefte für Mathematik 93, 127–140 (1982). https://doi.org/10.1007/BF01301400

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