# Trivial bundles of spaces of probability measures and countable-dimensionality

Studia Mathematica (1995)

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

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topGutev, 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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- [9] V. Gutev, Open mappings looking like projections, Set-Valued Anal. 1 (1993), 247-260. Zbl0818.54011
- [10] O.-H. Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), 748-758. Zbl57.1523.01
- [11] E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956), 233-238. Zbl0070.39502
- [12] E. Michael, Continuous selections I, Ann. of Math. 63 (1956), 361-382. Zbl0071.15902
- [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). Zbl0165.14603
- [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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