product of uniform spaces

Definition.

Let ${\{X_{\alpha }\}}_{\alpha \in I}$ be a nonempty family of uniform spaces. The is the weakest uniformity (http://planetmath.org/UniformitiesOnASetFormACompleteLattice) on the Cartesian product $X={\prod }_{\alpha \in I}{X}_{\alpha }$ making all the projection maps ${\pi }_{\alpha }:X\to X_{\alpha }$ uniformly continuous.

Title	product of uniform spaces
Canonical name	ProductOfUniformSpaces
Date of creation	2013-03-22 16:30:49
Last modified on	2013-03-22 16:30:49
Owner	mps (409)
Last modified by	mps (409)
Numerical id	4
Author	mps (409)
Entry type	Definition
Classification	msc 54E15