Sur un exemple de Banach et Kuratowski

• Autorzy: Robert Cauty
• Języki publikacji: FR

Abstrakty

EN

For A ⊂ I = [0,1], let $L_A$ be the set of continuous real-valued functions on I which vanish on a neighborhood of A. We prove that if A is an analytic subset which is not an $F_σ$ and whose closure has an empty interior, then $L_A$ is homeomorphic to the space of differentiable functions from I into ℝ.

Kategorie tematyczne

• 57N20: Topology of infinite-dimensional manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 3
• Strony: 195-207

Daty

wydano

1994

otrzymano

1990-06-18

poprawiono

1992-09-24

poprawiono

1993-07-20

Twórcy

autor

Robert Cauty

• 22, Rue Jouvenet 75016 Paris, France

Bibliografia

• [1] S. Banach et C. Kuratowski, Sur la structure des ensembles linéaires, Studia Math. 4 (1933), 95-99.
• [2] M. Bestvina and J. Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), 291-313.
• [3] R. Cauty, Caractérisation topologique de l'espace des fonctions dérivables, Fund. Math. 138 (1991), 35-58.
• [4] R. Cauty, T. Dobrowolski and W. Marciszewski, A contribution to the topological classification of the spaces $C_p(X)$, ibid. 142 (1993), 269-301.
• [5] D. Curtis and Nguyen To Nhu, Hyperspaces of finite subsets which are homeomorphic to $ℵ_0$-dimensional linear metric spaces, Topology Appl. 19 (1985), 251-260.
• [6] D. Curtis and R. M. Schori, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19-38.
• [7] W. Hurewicz, Relative perfekte Teile von Punktmengen und Mengen ( A), ibid. 12 (1928), 78-109.
• [8] C. Kuratowski, Topologie I, 4ème édition, PWN, Warszawa, 1958.
• [9] C. A. Rogers et al., Analytic Sets, Academic Press, London, 1980.
• [10] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $l_2$-manifolds, Fund. Math. 101 (1978), 93-110.