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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Duality relations for Lebesgue spaces of sections of vector bundles
The existence of a finite trivialising cover is a less stringent condition than one would expect: see Does every vector bundle allow a finite trivialization cover?
(Sorry for the commentlike answer b …
1
vote
Are there examples of compact infinite dimensional manifolds?
Yes. Compact Hilbert cube manifolds, for instance.
2
votes
why is this a sufficient condition for a domain to be a core of an unbounded operator?
See also Theorem VIII.11 in Reed-Simon (p.269 vol. 1).