Metric Space (Noun)
Meaning
A set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality.
Classification
Nouns denoting groupings of people or objects.
Examples
- A metric space is a fundamental concept in topology and analysis, providing a framework for studying geometric and topological properties of spaces.
- The Euclidean space is a classic example of a metric space, where the distance between two points is given by the Euclidean distance formula.
- In a metric space, the triangle inequality ensures that the distance between two points is always less than or equal to the sum of the distances between each point and a third point.
- A discrete metric space is a simple example of a metric space, where the distance between two distinct points is always 1, and the distance between a point and itself is 0.
- The concept of a metric space has been generalized to other areas of mathematics, such as functional analysis and probability theory, where it is used to study spaces of functions and probability measures.