Non-separable Hilbert manifolds of continuous mappings

Details Non-separable Hilbert manifolds of continuous mappings Non-separable Hilbert manifolds of continuous mappings

2006-10-06

arxiv.org/abs/math/0610214v2

Mathematics

General Topology

27 pages

Scientific paper

Let $X, Y$ be separable metrizable spaces, where $X$ is noncompact and $Y$ is equipped with an admissible complete metric $d$. We show that the space $C(X,Y)$ of continuous maps from $X$ into $Y$ equipped with the uniform topology is locally homeomorphic to the Hilbert space of weight $2^{\aleph_0}$ if (1) $(Y, d)$ is an ANRU, a uniform version of ANR and (2) the diameters of components of $Y$ is bounded away from zero. The same conclusion holds for the subspace $C_B(X,Y)$ of bounded maps if $Y$ is a connected complete Riemannian manifold.

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