Metric axioms and distance

Metric axioms and distance

Many mathematicians' experiences with distances in the settings of geometry, analysis, and topology can lead to the impression that the only worthwhile or ‘reasonable’ distance functions are metrics. We hope to convince the reader otherwise. Recall that a metric for a set X is a function d: X ×...

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Veröffentlicht in:Mathematical gazette 2011-11, Vol.95 (534), p.414-419
1. Verfasser: CULLINANE, MICHAEL J.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Axioms
Decimals
Distance functions
Highways
Mathematical functions
Toll bridges
Tolls
Topological spaces
Topology
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Beschreibung
Zusammenfassung:Many mathematicians' experiences with distances in the settings of geometry, analysis, and topology can lead to the impression that the only worthwhile or ‘reasonable’ distance functions are metrics. We hope to convince the reader otherwise. Recall that a metric for a set X is a function d: X × X → [0, ∞) satisfying all of the following metric axioms :
ISSN:0025-5572
2056-6328
DOI:10.1017/S0025557200003508