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.

In the Vinony graph

Within Vinony's link graph, metric space is referenced by 1,033 other articles, and connects out to continuous function, taxicab geometry and metrizable space.

It is catalogued under topics including Mathematical analysis, Mathematical structures and Metric spaces.

Its subject is documented across 64 Wikipedia language editions.

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

Encyclopedic overview

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

Excerpted from Wikipedia’s “metric space” article, available under the CC BY-SA 4.0 licence.