# 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 $\pi_{\alpha}\colon X\to X_{\alpha}$ uniformly continuous.

Title product of uniform spaces ProductOfUniformSpaces 2013-03-22 16:30:49 2013-03-22 16:30:49 mps (409) mps (409) 4 mps (409) Definition msc 54E15