Timeline for Category of Uniform spaces

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May 4, 2012 at 19:03	comment	added	Sergey Melikhov		The example in my answer, $\Bbb R^{I\times\Bbb R}\ne(\Bbb R^I)^{\Bbb R}$, has only complete uniform spaces. I didn't find an explicit example in the Rice-Tashjian paper, but they say that "the product $\times$ in Unif does not preserve sums (for example, $[0,1]\times\Bbb N$ is not the uniform sum of countably many copies of $[0,1]$) hence Unif is not cartasian-closed." This seems to hint that $X^{I\times\Bbb N}\ne(X^I)^{\Bbb N}$ in general, which also works for complete uniform spaces.
May 4, 2012 at 12:25	history	answered	David White	CC BY-SA 3.0