Difference between revisions of "Metric space"
DavidB4-bot (talk | contribs) (→top: clean up & uniformity) |
|||
| (4 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
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. | ||
| − | [[Category: Mathematics]] | + | 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. | ||
| + | |||
| + | [[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.