Friday, 9 September 2016

general topology - Bourbaki on the fact that continuous function on a compact is uniformly continuous

I am now looking theorem 2 in paragraph 4.1 of:



Bourbaki. "Elements of Mathematics General Topology. Part 1".



THEOREM 2. Every continuous mapping f of a compact space X into a uniform space X is uniformly continuous.




Now I realize that I don't understand the proof.



Could you present me a more detailed proof?

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