Infinite products which are Hilbert cubes
Author:
James E. West
Journal:
Trans. Amer. Math. Soc. 150 (1970), 125
MSC:
Primary 54.25
DOI:
https://doi.org/10.1090/S00029947197002661473
MathSciNet review:
0266147
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Abstract: Let $Q$ denote the Hilbert cube. It is shown that if $P$ and $P’$ are compact polyhedra of the same simple homotopy type then $P \times Q$ and $P’ \times Q$ are homeomorphic. A consequence of this result is that the Cartesian product of a countable, locally finite simplicial complex with a separable, infinitedimensional Fréchet space is a manifold modelled on the Fréchet space. It is also proved that a countably infinite product of nondegenerate spaces is a Hilbert cube provided that the product of each of the spaces with the Hilbert cube is a Hilbert cube. Together with the first result, this establishes that a countably infinite product of nondegenerate, compact, contractible polyhedra is a Hilbert 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 In addition, a proof is given of the (previously unpublished) theorem of R. D. Anderson that a countably infinite product of nondegenerate dendra is a Hilbert cube.

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Additional Information
Keywords:
Hilbert cube,
infinite product,
polyhedron,
simple homotopy type,
local homotopy negligibility,
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© Copyright 1970
American Mathematical Society