In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric. When a topological space has a topology that can be described by a metric, we say that the topological space is metrizable. In differential geometry, the word "metric" is also used to refer to a structure defined only on a vector space which is more properly termed a metric tensor (or Riemannian or pseudo-Riemannian metric).

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