PlanetMath: product of uniform spaces

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product of uniform spaces

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Definition Let $\{X_{\alpha}\}_{\alpha\in I}$ be a nonempty family of uniform spaces. The product of the uniform spaces is the weakest uniformity 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.

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Cross-references: uniformly continuous, projection maps, Cartesian product, uniform spaces

This is version 1 of product of uniform spaces, born on 2006-12-27.
Object id is 8691, canonical name is ProductOfUniformSpaces.
Accessed 699 times total.

Classification:

54E15 (General topology :: Spaces with richer structures :: Uniform structures and generalizations)

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