Difference between revisions of "Metric space"
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m (New page: A '''metric space''' is a pair (''X'', ''d'') where ''X'' is a topological space and ''d'' is a function mapping elements in ''M'' to real numbers, such that # ''d''(''x'', ''y'') ≥ ...) |
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| − | A '''metric space''' is a pair (''X'', ''d'') where ''X'' is a [[topological space]] and ''d'' is a | + | 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. | ||
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| + | [[Category:Mathematics]] | ||
| + | [[Category:Topology]] | ||
Latest revision as of 15:59, July 13, 2016
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.