Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T09:53:44.760Z Has data issue: false hasContentIssue false
  • English
  • Français

Metric axioms and distance

Published online by Cambridge University Press:  23 January 2015

Michael J. Cullinane
Michael J. Cullinane*
Affiliation:
Mathematics Department, Keene State College, Keene, New Hampshire, USA
Get access Rights & Permissions [Opens in a new window]

Extract

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:

Type
Articles
Information
The Mathematical Gazette , Volume 95 , Issue 534 , November 2011 , pp. 414 - 419
Copyright
Copyright © The Mathematical Association 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Hausdorff, F., Grundzüge der Mengenlehr (3rd edn.), de Gruyter, Leipzig (1938).Google Scholar
2. Nedev, S. I., o-metrizable spaces, Trans. Moscow Math. Soc. 24 (1971) pp. 213–247.Google Scholar
3. Gruenhage, G., Generalized metric spaces, in Handbook of set-theoretic topology, North-Holland (1984) pp. 423–501.Google Scholar
4. Abramsky, S., Domain theory in logical form, Annals of Pure and Applied Logic 51 (1991) pp. 1–77.Google Scholar
5. Scott, D., Outline of a mathematical theory of computation, in 4th Annual Princeton Conference on Information Sciences and Systems (1970) pp. 169–176.Google Scholar
6. Smyth, M. B., Topology, in Handbook of logic in computer science, Oxford University Press (1992) pp. 641–761.Google Scholar