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I know that the set $A$ of all the functions in $L^2[0,1]$ that are bounded by $1$ in the sup norm, $$ A = \{ f : f \in L^2[0,1], ||f||_{\infty} \leq 1\}, $$ has no interior points in $L^2([0,1])$. But, it is a convex and bounded subset of $L^2([0,1])$. Can someone recommend (if it exists) wha...
In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.
== Properties ==
Many basic constructions of the manifold theory, such as the tangent...
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