Function spaces in the Stegall class

Ivaylo S. Kortezov

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 259-270
  • ISSN: 0010-2628

Abstract

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We prove several stability properties for the class of compact Hausdorff spaces T such that C ( T ) with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.

How to cite

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Kortezov, Ivaylo S.. "Function spaces in the Stegall class." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 259-270. <http://eudml.org/doc/248378>.

@article{Kortezov1999,
abstract = {We prove several stability properties for the class of compact Hausdorff spaces $T$ such that $C(T)$ with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.},
author = {Kortezov, Ivaylo S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {usco mapping; minimal mapping; Stegall class; spaces of continuous functions; set-valued mapping; Stegall class; minimal upper semicontinuous mapping; stability properties},
language = {eng},
number = {2},
pages = {259-270},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Function spaces in the Stegall class},
url = {http://eudml.org/doc/248378},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Kortezov, Ivaylo S.
TI - Function spaces in the Stegall class
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 259
EP - 270
AB - We prove several stability properties for the class of compact Hausdorff spaces $T$ such that $C(T)$ with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.
LA - eng
KW - usco mapping; minimal mapping; Stegall class; spaces of continuous functions; set-valued mapping; Stegall class; minimal upper semicontinuous mapping; stability properties
UR - http://eudml.org/doc/248378
ER -

References

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  2. Bouziad A., Une classe d'espaces co-Namioka, C.R. de l'Acad. des Sci., Paris, t.310, série I, 1990, pp.779-782. MR1054296
  3. Bouziad A., The class of co-Namioka compact spaces is stable under product, Proc. Amer. Math. Soc. 194 3 (1996), 983-986. (1996) Zbl0844.54016MR1326999
  4. Fabian M., Gâteaux Differentiability of Convex Functions and Topology. Weak Asplund Spaces, John Wiley & Sons, Inc., 1997. Zbl0883.46011MR1461271
  5. Jayne J.E., Rogers C.A., Borel selectors for upper semi-continuous set-valued maps, Acta Math. 56 (1985), 41-7. (1985) Zbl0588.54020MR0793237
  6. Kenderov P.S., Orihuela J., A generic factorization theorem, Mathematika 42 (1995), 56-66. (1995) Zbl0827.54012MR1346672
  7. Kortezov I.S., Fragmentability of function spaces, preprint. 
  8. Oxtoby J.O., The Banach-Mazur game and Baire category theorem, in: Contributions to the Theory of Games, vol.III, Annals of Math. Studies 39, Princeton, N.J., 1957, pp.159-163. MR0093741
  9. Stegall Ch., A class of topological spaces and differentiability, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen 10 (1983), 63-77. (1983) MR0730947

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