Non-separable Hilbert Manifolds of Continuous Mappings

Using Toruńczyk’s charaterization theorem, we show that the space CB(X,Y ) of bounded continuous mappings from X into Y is a topological manifold modelled on the Hilbert space of weight 20 , with respect to the topology of uniform convergence, under the following three assumptions: (1) X is a noncompact, separable and metrizable space, (2) Y is a complete metric space which is an ANRU (ANR in uniform sense), (3) the components of Y have diameters bounded away from zero (compact polyhedra satisfy these assumptions (2) and (3) for Y ). The assumptions (2) and (3) can be replaced by “Y is a connected complete Riemannian manifold”.