Trivial bundles of spaces of probability measures and countable-dimensionality

Valentin Gutev

Studia Mathematica (1995)

  • Volume: 114, Issue: 1, page 1-11
  • ISSN: 0039-3223

Abstract

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The probability measure functor P carries open continuous mappings f : X o n t o → 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.

How to cite

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Gutev, Valentin. "Trivial bundles of spaces of probability measures and countable-dimensionality." Studia Mathematica 114.1 (1995): 1-11. <http://eudml.org/doc/216177>.

@article{Gutev1995,
abstract = {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.},
author = {Gutev, Valentin},
journal = {Studia Mathematica},
keywords = {countable-dimensional space; open mapping; set-valued mapping; selection; t(A)-approximate section; -approximate section; probability measure functor; compact metric spaces; -bundles},
language = {eng},
number = {1},
pages = {1-11},
title = {Trivial bundles of spaces of probability measures and countable-dimensionality},
url = {http://eudml.org/doc/216177},
volume = {114},
year = {1995},
}

TY - JOUR
AU - Gutev, Valentin
TI - Trivial bundles of spaces of probability measures and countable-dimensionality
JO - Studia Mathematica
PY - 1995
VL - 114
IS - 1
SP - 1
EP - 11
AB - 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.
LA - eng
KW - countable-dimensional space; open mapping; set-valued mapping; selection; t(A)-approximate section; -approximate section; probability measure functor; compact metric spaces; -bundles
UR - http://eudml.org/doc/216177
ER -

References

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  1. [1] P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory, Nauka, Moscow, 1973 (in Russian). 
  2. [2] S. Z. Ditor, Averaging operators in C(S) and lower semicontinuous sections of continuous maps, Trans. Amer. Math. Soc. 175 (1973), 195-208. Zbl0239.46050
  3. [3] A. N. Dranishnikov, On Q-fibrations without disjoint sections, Funktsional. Anal. i Prilozhen. 22 (2) (1988), 79-80 (in Russian). Zbl0653.55008
  4. [4] A. N. Dranishnikov, A fibration that does not accept two disjoint many-valued sections, Topology Appl. 35 (1990), 71-73. Zbl0715.54006
  5. [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. Zbl0632.46021
  6. [6] V. Fedorchuk, Soft mappings, set-valued retractions and functors, Uspekhi Mat. Nauk 41 (6) (1986), 121-159 (in Russian). 
  7. [7] V. Fedorchuk, A factorization lemma for open mappings between compact spaces, Mat. Zametki 42 (1) (1987), 101-113 (in Russian). Zbl0634.54010
  8. [8] V. Fedorchuk, Probability measures in topology, Uspekhi Mat. Nauk 46 (1) (1991), 41-80 (in Russian). Zbl0735.54033
  9. [9] V. Gutev, Open mappings looking like projections, Set-Valued Anal. 1 (1993), 247-260. Zbl0818.54011
  10. [10] O.-H. Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), 748-758. Zbl57.1523.01
  11. [11] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238. Zbl0070.39502
  12. [12] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382. Zbl0071.15902
  13. [13] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647-656. 
  14. [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. [15] A. Pełczyński, Linear extensions, linear averagings, and their applications to linear topological classification of spaces of continuous functions, Dissertationes Math. 58 (1968). Zbl0165.14603
  16. [16] H. Toruńczyk and J. West, Fibrations and bundles with Hilbert cube manifold fibers, Mem. Amer. Math. Soc. 406 (1989). Zbl0689.57013

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