Baire-one mappings contained in a usco map

Ondřej F. K. Kalenda

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 135-145
  • ISSN: 0010-2628

Abstract

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We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in ℝ d is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.

How to cite

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Kalenda, Ondřej F. K.. "Baire-one mappings contained in a usco map." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 135-145. <http://eudml.org/doc/250203>.

@article{Kalenda2007,
abstract = {We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in $\mathbb \{R\}^d$ is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.},
author = {Kalenda, Ondřej F. K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Baire-one function; usco map; usco-bounded sequence of continuous functions; Baire-one function; usco map; usco-bounded sequence of continuous functions},
language = {eng},
number = {1},
pages = {135-145},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Baire-one mappings contained in a usco map},
url = {http://eudml.org/doc/250203},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Kalenda, Ondřej F. K.
TI - Baire-one mappings contained in a usco map
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 135
EP - 145
AB - We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in $\mathbb {R}^d$ is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.
LA - eng
KW - Baire-one function; usco map; usco-bounded sequence of continuous functions; Baire-one function; usco map; usco-bounded sequence of continuous functions
UR - http://eudml.org/doc/250203
ER -

References

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  1. Anguelov R., Kalenda O., The convergence space of minimal usco mappings, preprint MATH-KMA-2006/197. MR2486619
  2. Fabian M., Gâteaux Differentiability of Convex Functions and Topology: Weak Asplund Spaces, Wiley-Interscience, New York, 1997. Zbl0883.46011MR1461271
  3. Hansell R.W., First class functions with values in nonseparable spaces, Constantin Carathéodory: an international tribute, Vol. I, II, World Sci. Publishing, Teaneck, NJ, 1991, pp.461-475. Zbl0767.54010MR1130849
  4. Hansell R.W., Jayne J.E., Talagrand M., First class selectors for weakly upper semi-continuous multi-valued maps in Banach spaces, J. Reine Angew. Math. 361 (1985), 201-220. (1985) Zbl0573.54012MR0807260
  5. Jayne J.E., Rogers C.A., Borel selectors for upper semi-continuous set-valued mappings, Acta Math. 155 (1985), 41-79. (1985) MR0793237
  6. Jayne J.E., Rogers C.A., Selectors, Princeton University Press, Princeton, 2002. Zbl1002.54001MR1915965
  7. Srivatsa V.V., Baire class 1 selectors for upper semicontinuous set-valued maps, Trans. Amer. Math. Soc. 337 (1993), 2 609-624. (1993) Zbl0822.54017MR1140919

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