Talk:Uniform space

I is said: "The topology induced by product of uniform spaces is the Tychonoff product of topologies induced by the uniform spaces." How to prove it? --VictorPorton 21:49, 22 May 2012 (CEST)

The product topology is the weakest topology that makes all projections continuous.

The product uniformity is the weakest uniformity that makes all projections uniformly continuous.

The topology generated by the product uniformity makes all projections continuous, since it makes them uniformly continuous. Thus, it is stronger than the product topology. It remains to check that it is weaker...

--Boris Tsirelson 22:33, 22 May 2012 (CEST)