Bounded metric space: Difference between revisions
(New page: {{metric space property}} ==Definition== A metric space is termed bounded if there exists a constant <math>D</math> such that the distance between any two points is at most <math>D</...) |
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A [[metric space]] is termed bounded if there exists a constant <math>D</math> such that the distance between any two points is at most <math>D</math>. The smallest such nonnegative constant <math>D</math> is termed the [[diameter of a metric space|diameter]]. | A [[metric space]] is termed bounded if there exists a constant <math>D</math> such that the distance between any two points is at most <math>D</math>. The smallest such nonnegative constant <math>D</math> is termed the [[diameter of a metric space|diameter]]. | ||
==Relation with other properties== | |||
===Stronger properties=== | |||
* [[Compact metric space]] | |||
* [[Totally bounded metric space]] | |||
Revision as of 00:17, 2 February 2008
This article defines a property that can be evaluated for a metric space
Definition
A metric space is termed bounded if there exists a constant such that the distance between any two points is at most . The smallest such nonnegative constant is termed the diameter.