Sur un exemple de Banach et Kuratowski

Robert Cauty

Fundamenta Mathematicae (1994)

  • Volume: 144, Issue: 3, page 195-207
  • ISSN: 0016-2736

Abstract

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For A ⊂ I = [0,1], let L A be the set of continuous real-valued functions on I which vanish on a neighborhood of A. We prove that if A is an analytic subset which is not an F σ and whose closure has an empty interior, then L A is homeomorphic to the space of differentiable functions from I into ℝ.

How to cite

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Cauty, Robert. "Sur un exemple de Banach et Kuratowski." Fundamenta Mathematicae 144.3 (1994): 195-207. <http://eudml.org/doc/212024>.

@article{Cauty1994,
author = {Cauty, Robert},
journal = {Fundamenta Mathematicae},
keywords = {analytic set; coanalytic set; non-Borelian; function space; hyperspace},
language = {fre},
number = {3},
pages = {195-207},
title = {Sur un exemple de Banach et Kuratowski},
url = {http://eudml.org/doc/212024},
volume = {144},
year = {1994},
}

TY - JOUR
AU - Cauty, Robert
TI - Sur un exemple de Banach et Kuratowski
JO - Fundamenta Mathematicae
PY - 1994
VL - 144
IS - 3
SP - 195
EP - 207
LA - fre
KW - analytic set; coanalytic set; non-Borelian; function space; hyperspace
UR - http://eudml.org/doc/212024
ER -

References

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  1. [1] S. Banach et C. Kuratowski, Sur la structure des ensembles linéaires, Studia Math. 4 (1933), 95-99. 
  2. [2] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313. Zbl0629.54011
  3. [3] R. Cauty, Caractérisation topologique de l'espace des fonctions dérivables, Fund. Math. 138 (1991), 35-58. Zbl0770.54015
  4. [4] R. Cauty, T. Dobrowolski and W. Marciszewski, A contribution to the topological classification of the spaces C p ( X ) , ibid. 142 (1993), 269-301. Zbl0813.54009
  5. [5] D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to ℵ 0 -dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260. Zbl0587.54015
  6. [6] D. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19-38. Zbl0409.54044
  7. [7] W. Hurewicz, Relative perfekte Teile von Punktmengen und Mengen ( A), ibid. 12 (1928), 78-109. Zbl54.0097.06
  8. [8] C. Kuratowski, Topologie I, 4ème édition, PWN, Warszawa, 1958. 
  9. [9] C. A. Rogers et al., Analytic Sets, Academic Press, London, 1980. 
  10. [10] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of l 2 -manifolds, Fund. Math. 101 (1978), 93-110. Zbl0406.55003

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