Even though the topological structure of Fr�chet spaces is more complicated than that of Banach spaces due to the lack of a norm, many important results in functional analysis, like the Hahn Banach theorem, the open mapping theorem, and the Banach Steinhaus theorem, still hold.
12.
But then we would have a linear continuous bijection T : ! " ?! " c " 0, hence invertible by the open mapping theorem, which is impossible, because ! " and " c " 0 are not even homeomorphic ( the latter is separable, whereas the former is not ).
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:: Just for my knowledge, can someone please help me understand why that integral is continuous in q ? ( Nevermind on that, I actually found this in my book finally . . . and it's in the proof of the open mapping theorem, which makes sense . ) Thanks for the help ! talk ) 14 : 08, 25 April 2009 ( UTC)
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