Un exemple d'ensembles absorbants non équivalents

Robert Cauty

Fundamenta Mathematicae (1991)

  • Volume: 140, Issue: 1, page 49-61
  • ISSN: 0016-2736

Abstract

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We give an example in the Hilbert space ℓ 2 of two subsets which are absorbing for the class of topologically complete spaces, but for which there exists no homeomorphism of ℓ 2 onto itself mapping one of these subsets onto the other.

How to cite

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Cauty, Robert. "Un exemple d'ensembles absorbants non équivalents." Fundamenta Mathematicae 140.1 (1991): 49-61. <http://eudml.org/doc/211928>.

@article{Cauty1991,
author = {Cauty, Robert},
journal = {Fundamenta Mathematicae},
keywords = {nonequivalent absorbing sets; topologically complete spaces; homeomorphisms},
language = {fre},
number = {1},
pages = {49-61},
title = {Un exemple d'ensembles absorbants non équivalents},
url = {http://eudml.org/doc/211928},
volume = {140},
year = {1991},
}

TY - JOUR
AU - Cauty, Robert
TI - Un exemple d'ensembles absorbants non équivalents
JO - Fundamenta Mathematicae
PY - 1991
VL - 140
IS - 1
SP - 49
EP - 61
LA - fre
KW - nonequivalent absorbing sets; topologically complete spaces; homeomorphisms
UR - http://eudml.org/doc/211928
ER -

References

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  1. [1] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975. 
  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., à paraître. Zbl0770.54015
  4. [4] R. Cauty, Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de ℒ 1 , ibid., à paraître. 
  5. [5] R. Cauty, Sur deux espaces de fonctions non dérivables, prépublication, 1990. 
  6. [6] T. Dobrowolski, W. Marciszewski and J. Mogilski, On topological classification of function spaces C p X of low Borel complexity, preprint, 1989. Zbl0768.54016
  7. [7] S. Mazur und L. Sternbach, Über die Borelschen Typen von linearen Mengen, Studia Math. 4 (1933), 48-53. Zbl0008.31503
  8. [8] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of l 2 -manifolds, Fund. Math. 101 (1978), 93-110. Zbl0406.55003
  9. [9] H. Toruńczyk, Absolute retracts as factors of normed linear spaces, ibid. 86 (1974), 53-67. Zbl0318.57005

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