Probability measure functors preserving the ANR-property of metric spaces

Authors:
Nguyen To Nhu and Ta Khac Cu

Journal:
Proc. Amer. Math. Soc. **106** (1989), 493-501

MSC:
Primary 60B05; Secondary 46E27, 54C55

DOI:
https://doi.org/10.1090/S0002-9939-1989-0964459-9

MathSciNet review:
964459

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the set of all probability measures on a metric space whose supports consist of no more than points, equipped with the Fedorchuk topology. We prove that if then for every . This implies that for each the functor preserves the topology of separable Hilbert space.

**[BP]**C. Bessaga and A. Pelczynski,*Selected topics in infinite dimensional topology*, Warszawa 1975. MR**0478168 (57:17657)****[DT]**T. Dobrowolski and H. Torunczyk,*Separable complete ANR's admitting a group structure are Hilbert manifolds*, Topology Appl.**12**(1984), 229-235. MR**623731 (83a:58007)****[Fe]**V. V. Fedorchuk,*Probability measures and absolute neighborhood retracts*, Soviet Math. Dokl.**22**(1980), 849-853.**[Fr]**A. H. Frink,*Distance functions and the metrization problem*, Bull. Amer. Math. Soc.**43**(1937), 133-142. MR**1563501****[M]**H. W. Martin,*A note on Frink metrization theorem*, Rocky Mountain J. Math.**6**(1976), 155-157. MR**0391035 (52:11857)****[N1]**Nguyen To Nhu,*Investigating the ANR-property of metric spaces*, Fund. Math.**124**(1984), 243-254. MR**774515 (86d:54018)****[N2]**-,*Hyperspaces of compact sets in metric linear spaces*, Topology Appl.**22**(1986), 109-122. MR**836318 (87e:54027)****[N3]**-,*Orbit spaces of finite groups acting linearly on normed spaces*, Bull. Ac. Pol. Math.**32**(1986), 417-424. MR**782757 (86f:54029)****[T]**H. Torunczyk,*Characterizing Hilbert space topology*, Fund. Math.**111**(1981), 247-262. MR**611763 (82i:57016)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1989-0964459-9

Keywords:
ANR,
probability measure,
Hilbert space

Article copyright:
© Copyright 1989
American Mathematical Society