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.
@article{bwmeta1.element.bwnjournal-article-fmv140i1p49bwm,
author = {Robert Cauty},
title = {Un exemple d'ensembles absorbants non \'equivalents},
journal = {Fundamenta Mathematicae},
volume = {138},
year = {1991},
pages = {49-61},
language = {fr},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv140i1p49bwm}
}
Cauty, Robert. Un exemple d'ensembles absorbants non équivalents. Fundamenta Mathematicae, Tome 138 (1991) pp. 49-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i1p49bwm/
[00000] [1] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975.
[00001] [2] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313. | Zbl 0629.54011
[00002] [3] R. Cauty, Caractérisation topologique de l'espace des fonctions dérivables, Fund. Math., à paraître. | Zbl 0770.54015
[00003] [4] R. Cauty, Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de , ibid., à paraître.
[00004] [5] R. Cauty, Sur deux espaces de fonctions non dérivables, prépublication, 1990.
[00005] [6] T. Dobrowolski, W. Marciszewski and J. Mogilski, On topological classification of function spaces of low Borel complexity, preprint, 1989. | Zbl 0768.54016
[00006] [7] S. Mazur und L. Sternbach, Über die Borelschen Typen von linearen Mengen, Studia Math. 4 (1933), 48-53. | Zbl 0008.31503
[00007] [8] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of -manifolds, Fund. Math. 101 (1978), 93-110. | Zbl 0406.55003
[00008] [9] H. Toruńczyk, Absolute retracts as factors of normed linear spaces, ibid. 86 (1974), 53-67. | Zbl 0318.57005