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Wikipedia definition
1. Metric (mathematics)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. A topological space whose topology can be described by a metric is called metrizable.
Read “Metric (mathematics)” on English Wikipedia
Read “距離函数” on Japanese Wikipedia
Read “Metric (mathematics)” on DBpedia

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