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>>634 > >>633 追加 > 正直わからん > http://math.stackexchange.com/questions/58548/why-are-vec tor-spaces-not-isomorphic-to-their-duals/58598#58598 > 8. answered Aug 19 '11 at 21:07 MartianInvader > (抜粋) > > And a finite linear combination of things that have finite-dimensional support will still have finite-dimensional support, and thus can't send infinitely many independent vect ors all to 1. > > What you need is a notion of convergence if you want to add infinitely many things, which isn't always obvious how to define. > > In the end, it boils down to a cardinality issue - not of the vect or spaces themselves, but of the dimensions. In the example you give, R＾<ω has countably infinite dimension, but the dimension of its dual is uncountable.
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