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The group of measure preserving transformations of the unit interval is an absolute retract


Author: Nguyen To Nhu
Journal: Proc. Amer. Math. Soc. 110 (1990), 515-522
MSC: Primary 28D15; Secondary 54C55, 58D07
DOI: https://doi.org/10.1090/S0002-9939-1990-1009997-6
MathSciNet review: 1009997
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Abstract | References | Similar Articles | Additional Information

Abstract: The group of measure preserving transformations of the unit interval equipped with the weak topology is an absolute retract, hence is homeomorphic to a separable Hilbert space.


References [Enhancements On Off] (What's this?)

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  • [K] M. Keane, Contractibility of the automorphism group of a nonatomic measure space, Proc. Amer. Math. Soc. 26 (1970), 420-422. MR 0265555 (42:464)
  • [N] N. T. Nhu, Investigating the ANR-property of metric spaces, Fund. Math. 124 (1984), 243-254. MR 774515 (86d:54018)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1009997-6
Keywords: Measure preserving transformations, absolute retract, Hilbert space
Article copyright: © Copyright 1990 American Mathematical Society

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