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

A Quasi-Metric Topology Compatible with Inclusion Monotonicity on Interval Space 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

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

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1997 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009935210180
Publisher site
See Article on Publisher Site

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