A mapping theorem for Hilbert cube manifolds

Prasad, V. S.

doi:10.1090/S0002-9939-1983-0691301-0

A mapping theorem for Hilbert cube manifolds
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Proc. Amer. Math. Soc. 88 (1983), 165-168 Request permission

Abstract:

We show that every compact connected Hilbert cube manifold $M$ can be obtained from the Hilbert cube $Q$ by making identifications on a face of $Q$. Some applications of this result to measure preserving homeomorphisms on $M$ are given: (1) The first is concerned with which measures on $M$ are equivalent to each other by homeomorphisms. (2) The second application is about approximating invertible Borel measurable transformations of $M$ by measure preserving homeomorphisms of $M$. (3) The final application is concerned with generic properties of measure preserving homeomorphisms of $M$.

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