pseudometric space
A pseudometric space is a set together with a non-negative real-valued function (called a pseudometric) such that, for every ,
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In other words, a pseudometric space is a generalization of a metric space in which we allow the possibility that for distinct values of and .
References
- 1 L.A. Steen, J.A.Seebach, Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970.
Title | pseudometric space |
Canonical name | PseudometricSpace |
Date of creation | 2013-03-22 14:40:18 |
Last modified on | 2013-03-22 14:40:18 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 7 |
Author | mathcam (2727) |
Entry type | Definition |
Classification | msc 54E35 |
Synonym | pesudo-metric space |
Related topic | MetricSpace |
Related topic | QuasimetricSpace |
Related topic | NormedVectorSpace |
Related topic | Seminorm |
Defines | pseudometric |
Defines | pseudo-metric |