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 of two subsets which are absorbing for the class of topologically complete spaces, but for which there exists no homeomorphism of 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 , 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 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 -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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