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. 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.