metric space

set equipped with a metric (distance function)

AI overview

A metric space is a collection of objects with a way to measure the distance between any two of them. This concept matters because it provides a unified framework for studying properties like closeness and continuity that appear across mathematics, physics, and other fields.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Show 2 more facts

Commons category: Metric geometry
Stack Exchange tag: physics.stackexchange.com/tags/metric-space

Sources (5)

via Wikidata · CC0

~40 min read

Article

The plane (a set of points) can be equipped with different metrics. In the taxicab metric the red, yellow and blue paths have the same length (12), and are all shortest paths. In the Euclidean metric, the green path has length