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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
3
votes
Can we define smooth diffeomorphisms on the Hilbert cube $[0,1]^\mathbb{N}$ ? Has it been do...
An addendum to what wrote Peter Michor above: Frölicher spaces identify naturally with the full subcategory of reflexive diffeological spaces. (exercises 79 and 80 of the book). So, for your space equ …
1
vote
Why the name 'separable' space?
Well "séparer" means just "disjoin", "split up" etc. There are few meanings for "séparation" in french. For exemple "séparer par des fonctions". If you have a space $X$ and a set of functions ${\cal F …