Metric space

related topics
{math, number, function}
{math, energy, light}
{area, part, region}

In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined.

The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them.

The geometric properties of the space depend on the metric chosen, and by using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.

A metric space also induces topological properties like open and closed sets which leads to the study of even more abstract topological spaces.

Contents

Full article ▸

related documents
Set (mathematics)
Operator
Taylor's theorem
Interpolation
Dirac delta function
Extended Euclidean algorithm
Exponential function
Monoid
Template (programming)
Cholesky decomposition
Hausdorff dimension
Semidirect product
Square root
Integer
Icon (programming language)
Riemannian manifold
Kernel (matrix)
Vigenère cipher
Communication complexity
Tail recursion
Cantor's diagonal argument
Equivalence relation
Category theory
Standard ML
Supremum
Complete metric space
L'Hôpital's rule
Insertion sort
P = NP problem
PL/SQL