# Examples of Uniform Spaces

Are there any important examples of uniform spaces other than metric spaces and topological groups?

Also, what is an example of when the uniform structure of topological groups is used?

A simple example: $[0,1]^I$ is a uniform space (as a product of metric, hence uniform, spaces). And it's not metrisable if $I$ is uncountable and it's not a topological group as it has the FPP.
• Why $[0,1]^I$ has the FPP? – G. Ottaviano Aug 16 '18 at 22:40
• @G.Ottaviano It's a classic well-known fact. It extends Brouwer's fp theorem for finite $I$. – Henno Brandsma Aug 16 '18 at 22:48
Examples arbitrary commact Hausdorff spaces, that have a unique uniformity. This example is very interesting, in that it allows to talk about uniform continuity for maps $X\to C$, where, say $X$ is metric and $C$ is compact.