Difference between revisions of "Metric space"
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A '''metric space''' is a pair (''X'', ''d'') where ''X'' is a [[topological space]] and ''d'' is a [[Metric (mathematics)|metric]]. All metric spaces are [[Hausdorff space]]s. | A '''metric space''' is a pair (''X'', ''d'') where ''X'' is a [[topological space]] and ''d'' is a [[Metric (mathematics)|metric]]. All metric spaces are [[Hausdorff space]]s. | ||
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| + | Examples of metric spaces include: | ||
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| + | *the set of [[real numbers]] | ||
| + | *a Euclidean space of any dimension | ||
| + | *any set of finite points where the distance between distinct points is defined as 1, and the distance between a point and itself is defined as zero. | ||
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
[[category: Topology]] | [[category: Topology]] | ||
Revision as of 02:02, July 6, 2007
A metric space is a pair (X, d) where X is a topological space and d is a metric. All metric spaces are Hausdorff spaces.
Examples of metric spaces include:
- the set of real numbers
- a Euclidean space of any dimension
- any set of finite points where the distance between distinct points is defined as 1, and the distance between a point and itself is defined as zero.