Sur deux espaces de fonctions non dérivables
Cauty, Robert
Fundamenta Mathematicae, Tome 141 (1992), p. 195-214 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let D (resp. D*) be the subspace of C = C([0,1], R) consisting of differentiable functions (resp. of functions differentiable at the one point at least). We give topological characterizations of the pairs (C, D) and (C, D*) and use them to give some examples of spaces homeomorphic to CDor to CD*.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:211960 
@article{bwmeta1.element.bwnjournal-article-fmv141i3p195bwm,
     author = {Robert Cauty},
     title = {Sur deux espaces de fonctions non d\'erivables},
     journal = {Fundamenta Mathematicae},
     volume = {141},
     year = {1992},
     pages = {195-214},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p195bwm}
}

Cauty, Robert. Sur deux espaces de fonctions non dérivables. Fundamenta Mathematicae, Tome 141 (1992) pp. 195-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i3p195bwm/

[00000] [1] R. D. Anderson and J. D. McCharen, On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283-289. | Zbl 0203.25805

[00001] [2] N. K. Bary, A Treatise on Trigonometric Series, Vol. I, Pergamon Press, Oxford 1964. | Zbl 0129.28002

[00002] [3] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975.

[00003] [4] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313. | Zbl 0629.54011

[00004] [5] R. Cauty, Caractérisation topologique de l'espace des fonctions dérivables, Fund. Math. 138 (1991), 35-58. | Zbl 0770.54015

[00005] [6] R. Cauty, Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de ℒ1, ibid. 139 (1991), 23-36.

[00006] [7] D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to ℵ0-dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260. | Zbl 0587.54015

[00007] [8] A. S. Kechris, Sets of everywhere singular functions, in: Recursion Theory Week, H.D. Ebbinghaus et al. (eds.), Lecture Notes in Math. 1141, Springer, Berlin 1985, 233-244.

[00008] [9] C. Kuratowski, Topologie I, 4e édition, PWN, Warszawa 1958.

[00009] [10] S. Mazur und L. Sternbach, Über die Borelschen Typen von linearen Mengen, Studia Math. 4 (1933), 48-53. | Zbl 0008.31503

[00010] [11] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of l2-manifolds, Fund. Math. 101 (1978), 93-110. | Zbl 0406.55003