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A mapping theorem for Hilbert cube manifolds

Author: V. S. Prasad
Journal: Proc. Amer. Math. Soc. 88 (1983), 165-168
MSC: Primary 58C35; Secondary 28C15, 57N20
MathSciNet review: 691301
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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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Keywords: Hilbert cube manifold, measure preserving homeomorphism
Article copyright: © Copyright 1983 American Mathematical Society

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