ArticleOriginal scientific text
Title
Sur deux espaces de fonctions non dérivables
Authors 1
Affiliations
- 22, Rue Jouvenet, 75016 Paris, France
Abstract
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 C\D or to C\D*.
Bibliography
- R. D. Anderson and J. D. McCharen, On extending homeomorphisms to Fréchet manifolds, Proc. Amer. Math. Soc. 25 (1970), 283-289.
- N. K. Bary, A Treatise on Trigonometric Series, Vol. I, Pergamon Press, Oxford 1964.
- C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, PWN, Warszawa 1975.
- M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313.
- R. Cauty, Caractérisation topologique de l'espace des fonctions dérivables, Fund. Math. 138 (1991), 35-58.
- R. Cauty, Les fonctions continues et les fonctions intégrables au sens de Riemann comme sous-espaces de
- D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to
- 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.
- C. Kuratowski, Topologie I, 4e édition, PWN, Warszawa 1958.
- S. Mazur und L. Sternbach, Über die Borelschen Typen von linearen Mengen, Studia Math. 4 (1933), 48-53.
- H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14131.pdf
Pages:
195-214
Main language of publication
French
Received
1990-06-25
Accepted
1992-04-09
Published
1992
Exact and natural sciences