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I'm looking for a reference to cite regarding the property presented in the title: "Closed and bounded sets of a nuclear Fréchet space are compact"

Thank you in advance for the help!

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3 Answers

up vote 4 down vote accepted

Have a look at Proposition 50.2 in

F. Treves: Topological Vectors Spaces, Distributions and Kernels, Academic Press 1995 or Dover 2006

Statement (50.12) in that proposition is precisely what you need.

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Thank you for your quick answer! –  Loïc Teyssier Sep 20 '12 at 13:02
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Maybe not in a single theorem, but you can go for Cor1 in Section 33 and Cor3 in Section 50 in Treves book.

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Thanks for your answer, but I guess Liviu narrowed down a more precise reference, I guess! –  Loïc Teyssier Sep 20 '12 at 13:04
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and he was a couple of second faster :) –  Stefan Waldmann Sep 20 '12 at 13:05
    
By accident, I had Treves' book right by my side. –  Liviu Nicolaescu Sep 20 '12 at 13:12
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does Wikipedia qualify as a reference? for a historical overview, see A pedagogical history of compactness

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Wikipedia is the place where I actually stumbled across the result... the problem is that I doubt wikipedia qualifies as an academic source in an article. Anyway, I prefer not. Thanks anyway! –  Loïc Teyssier Sep 20 '12 at 13:03
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