Metric axioms and distance
Michael J. Cullinane · The Mathematical Gazette · 2011
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: