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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

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Can we define smooth diffeomorphisms on the Hilbert cube $[0,1]^\mathbb{N}$ ? Has it been do...

Can we define smooth diffeomorphisms on the Hilbert cube$[0,1]^\mathbb{N}$ ? Has it been done in the literature? For example, let $E$ be the set of bijections $f$ of the Hilbert cube, such that $f((x …