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Infinite Products which are Hilbert Cubes

1970; American Mathematical Society; Volume: 150; Issue: 1 Linguagem: Inglês

10.2307/1995478

1088-6850

James E. West,

Topological and Geometric Data Analysis

Let Q denote the Hubert cube.It is shown that if P and P' are compact polyhedra of the same simple homotopy type then Px Q and P' x Q are homeomorphic.A consequence of this result is that the Cartesian product of a countable, locally finite simplicial complex with a separable, infinite-dimensional Fréchet space is a manifold modelled on the Fréchet space.It is also proved that a countably infinite product of nondegenerate spaces is a Hubert cube provided that the product of each of the spaces with the Hubert cube is a Hubert cube.Together with the first result, this establishes that a countably infinite product of nondegenerate, compact, contractible polyhedra is a Hubert cube.In addition, a proof is given of the (previously unpublished) theorem of R. D. Anderson that a countably infinite product of nondegenerate dendra is a Hubert cube.