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A Quasi-Metric Topology Compatible with Inclusion Monotonicity on Interval Space

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Reliable Computing

Abstract

It is well known that the metric topology [8] on interval space is not compatible with the interval inclusion monotonicity property in the sense that there may exist monotonic functions which are not continuous and conversely. This paper provides a quasi-metric topology for the interval space consistent with the real line topology and whose continuous functions are exactly the monotonic ones. The provided quasi-metric is not a metric only because it fails to satisfy the symmetrical property. The quoted title is due to the fact that except to the Hausdorff property of the metric-which does not fit for our point of view-the other good metric properties remain.

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Authors and Affiliations

  1. Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte-UFRN, Campus Universitário-Lagoa Nova, 59.072-970, Natal-RN, Brasil

    Benedito Melo Acióly & Benjamín R. Callejas Bedregal

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  1. Benedito Melo Acióly
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  2. Benjamín R. Callejas Bedregal
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Acióly, B.M., Callejas Bedregal, B.R. A Quasi-Metric Topology Compatible with Inclusion Monotonicity on Interval Space. Reliable Computing 3, 305–313 (1997). https://doi.org/10.1023/A:1009935210180

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  • DOI: https://doi.org/10.1023/A:1009935210180

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