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ArticleOriginal scientific text

Title

Trivial bundles of spaces of probability measures and countable-dimensionality

Authors 1

Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bontchev Str., Bl. 8, 1113 Sofia, Bulgaria

Abstract

The probability measure functor P carries open continuous mappings f:Xon→→Y of compact metric spaces into Q-bundles provided Y is countable-dimensional and all fibers f-1(y) are infinite. This answers a question raised by V. Fedorchuk.

Keywords

ENG
countable-dimensional space, open mapping, set-valued mapping, selection, t(A)-approximate section

Bibliography

  1. P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian).
  2. S. Z. Ditor, Averaging operators in C(S) and lower semicontinuous sections of continuous maps, Trans. Amer. Math. Soc. 175 (1973), 195-208.
  3. A. N. Dranishnikov, On Q-fibrations without disjoint sections, Funktsional. Anal. i Prilozhen. 22 (2) (1988), 79-80 (in Russian).
  4. A. N. Dranishnikov, A fibration that does not accept two disjoint many-valued sections, Topology Appl. 35 (1990), 71-73.
  5. V. Fedorchuk, Trivial bundles of spaces of probability measures, Mat. Sb. 129 (171) (1986), 473-493 (in Russian); English transl.: Math. USSR-Sb. 57 (1987), 485-505.
  6. V. Fedorchuk, Soft mappings, set-valued retractions and functors, Uspekhi Mat. Nauk 41 (6) (1986), 121-159 (in Russian).
  7. V. Fedorchuk, A factorization lemma for open mappings between compact spaces, Mat. Zametki 42 (1) (1987), 101-113 (in Russian).
  8. V. Fedorchuk, Probability measures in topology, Uspekhi Mat. Nauk 46 (1) (1991), 41-80 (in Russian).
  9. V. Gutev, Open mappings looking like projections, Set-Valued Anal. 1 (1993), 247-260.
  10. O.-H. Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), 748-758.
  11. E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238.
  12. E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382.
  13. E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-656.
  14. A. A. Milyutin, Isomorphisms of the spaces of continuous functions over compact sets of the cardinality of the continuum, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 2 (1966), 150-156 (in Russian).
  15. A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. 58 (1968).
  16. H. Toruńczyk and J. West, Fibrations and bundles with Hilbert cube manifold fibers, Mem. Amer. Math. Soc. 406 (1989).
Studia Mathematica
1995/114/1
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Pages:
1-11
Main language of publication
English
Received
1992-10-05
Accepted
1995-01-30
Published
1995
Exact and natural sciences