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1995 | 114 | 1 | 1-11
Tytuł artykułu

Trivial bundles of spaces of probability measures and countable-dimensionality

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The probability measure functor P carries open continuous mappings $f: X onto → Y$ 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.
Twórcy
  • Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bontchev Str., Bl. 8, 1113 Sofia, Bulgaria, gutev@bgcict.bitnet
Bibliografia
  • [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).
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