# What is metric space?

• (noun): 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.

## Metric Space

A metric space is an ordered pair where is a set and is a metric on, i.e., a function

### Some articles on metric space:

Convex Metric Space
... In mathematics, convex metric spaces are, intuitively, metric spaces with the property any "segment" joining two points in that space has other points in it besides the ... Formally, consider a metric space (X, d) and let x and y be two points in X ... A convex metric space is a metric space (X, d) such that, for any two distinct points x and y in X, there exists a third point z in X lying between x and y ...
Limit Set - Definition For Iterated Functions
... Let be a metric space, and let be a continuous function ... The closure is here needed, since we have not assumed that the underlying metric space of interest to be a complete metric space ...
Minkowski–Bouligand Dimension - Alternative Definitions
... is that this definition generalizes to any metric space ... assume the fractal is contained in a Euclidean space, and define boxes according to the external structure "imposed" by the containing space ... that they measure the amount of "disorder" in the metric space or fractal at scale, and also measure how many "bits" one would need to describe an ...
Completed - Mathematical Completeness
... It may be described equivalently as either the completeness of R as metric space or as a partially ordered set (see below) ... A metric space is complete if every Cauchy sequence in it converges ... See Complete metric space ...
Generalizations of Metric Spaces - Metric Spaces As Enriched Categories
... Every metric space can now be viewed as a category enriched over Set For each set The composition morphism will be the unique morphism in given from the triangle inequality The identity morphism will be ...

### Famous quotes containing the word space:

At first thy little being came:
If nothing once, you nothing lose,
For when you die you are the same;
The space between, is but an hour,
The frail duration of a flower.
Philip Freneau (1752–1832)