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

DOI:
https://doi.org/10.1090/S0002-9939-1983-0691301-0

MathSciNet review:
691301

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

**[A]**Steve Alpern,*Approximation to and by measure preserving homeomorphisms*, J. London Math. Soc. (2)**18**(1978), no. 2, 305–315. MR**509946**, https://doi.org/10.1112/jlms/s2-18.2.305**[A]**Steve Alpern,*Generic properties of measure preserving homeomorphisms*, Ergodic theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1978), Lecture Notes in Math., vol. 729, Springer, Berlin, 1979, pp. 16–27. MR**550406****[B]**Morton Brown,*A mapping theorem for untriangulated manifolds*, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 92–94. MR**0158374****[C]**T. A. Chapman,*Lectures on Hilbert cube manifolds*, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR**0423357****[C-V]**Charles O. Christenson and William L. Voxman,*Aspects of topology*, Marcel Dekker, Inc., New York-Basel, 1977. Pure and applied Mathematics, Vol. 39. MR**0487938****[O-P]**John C. Oxtoby and Vidhu S. Prasad,*Homeomorphic measures in the Hilbert cube*, Pacific J. Math.**77**(1978), no. 2, 483–497. MR**510936**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1983-0691301-0

Keywords:
Hilbert cube manifold,
measure preserving homeomorphism

Article copyright:
© Copyright 1983
American Mathematical Society