uniform structure of a metric space

Let (X,d) be a metric space. There is a natural uniform structure on X, which induces the same topologyMathworldPlanetmath as the metric. We define a subset V of the Cartesian product X×X to be an entourage if and only if it contains a subset of the form


for some ε.

Title uniform structure of a metric space
Canonical name UniformStructureOfAMetricSpace
Date of creation 2013-03-22 12:47:18
Last modified on 2013-03-22 12:47:18
Owner n3o (216)
Last modified by n3o (216)
Numerical id 6
Author n3o (216)
Entry type Derivation
Classification msc 54E15