L’espace des fonctions continues d’un espace métrique dénombrable
HTML articles powered by AMS MathViewer
- by Robert Cauty PDF
- Proc. Amer. Math. Soc. 113 (1991), 493-501 Request permission
Abstract:
We prove that, for any countable nondiscrete metric space $X$, the space of continuous real-valued functions on $X$, with the topology of pointwise convergence, and its subspace of bounded functions, are both homeomorphic to ${\sigma _\omega }$, the countably infinite product of copies of $l_f^2$.References
- Mladen Bestvina and Jerzy Mogilski, Characterizing certain incomplete infinite-dimensional absolute retracts, Michigan Math. J. 33 (1986), no. 3, 291–313. MR 856522, DOI 10.1307/mmj/1029003410
- J. Dijkstra, T. Grilliot, D. Lutzer, and J. van Mill, Function spaces of low Borel complexity, Proc. Amer. Math. Soc. 94 (1985), no. 4, 703–710. MR 792287, DOI 10.1090/S0002-9939-1985-0792287-2 C. Kuratowski, Topologie. II, 3e édition, PWN, Warszawa, 1961.
- J. van Mill, Topological equivalence of certain function spaces, Compositio Math. 63 (1987), no. 2, 159–188. MR 906368
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 493-501
- MSC: Primary 54C35; Secondary 57N17
- DOI: https://doi.org/10.1090/S0002-9939-1991-1075943-3
- MathSciNet review: 1075943