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
HTML articles powered by AMS MathViewer

by V. S. Prasad

Proc. Amer. Math. Soc. 88 (1983), 165-168

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

PDF | 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 $M$.

References

Steve Alpern, Approximation to and by measure preserving homeomorphisms, J. London Math. Soc. (2) 18 (1978), no. 2, 305–315. MR 509946, DOI 10.1112/jlms/s2-18.2.305
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
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
T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357
Charles O. Christenson and William L. Voxman, Aspects of topology, Pure and Applied Mathematics, Vol. 39, Marcel Dekker, Inc., New York-Basel, 1977. MR 0487938
John C. Oxtoby and Vidhu S. Prasad, Homeomorphic measures in the Hilbert cube, Pacific J. Math. 77 (1978), no. 2, 483–497. MR 510936