Difference between revisions of "Metric space"
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*the set of [[real numbers]] | *the set of [[real numbers]] | ||
| − | *a Euclidean space of any dimension | + | *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. | *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 19:46, May 24, 2008
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.