A continuous map from a T2 & compact space to a uniform space is uniformly continuous.

Can you recommend some literature that give a proof of this statement, and who allegedly prove it first?

BTW, is there any use of uniform spaces or topological spaces in mathematical (or theoretical) physics?

Thanks.

flag	asked Nov 17 2011 at 20:53 Alan 202●7

I think you can find this in Kelley's General topology. – Benjamin Steinberg Nov 17 2011 at 20:57

It is in the general topology book of Bourbaki. If that is not the first published proof, it is probably in the paper of Andre Weil that introduced uniform space as entourages. – Michael Greinecker Nov 17 2011 at 21:27

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