DagSemProc.04351.22.pdf
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What do partial metrics represent?
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Dagstuhl Seminar Proceedings, Volume 4351
Series: Dagstuhl Seminar Proceedings (DagSemProc) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2005-04-22
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Ralph Kopperman, Steve Matthews, and Homeira Pajoohesh. What do partial metrics represent?. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.04351.22
https://doi.org/10.4230/DagSemProc.04351.22
Abstract
Partial metrics were introduced in 1992
as a metric to allow the distance of a point from
itself to be non zero. This notion of self distance, designed to extend
metrical concepts to Scott topologies as used
in computing, has little intuition for the mainstream Hausdorff topologist.
The talk will show that a partial metric over a set can be represented by a metric over that set with a so-called 'base point'.
Thus we establish that a partial metric is essentially a structure combining both a metric space and a skewed view of that space from the base point. From this we can deduce what it is that partial metrics are really all about.
Keywords
- Metric
- partial metric
- base point
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