References
Anderson, R. D.: Topological properties of the Hilbert cube and the infinite product of open intervals. Trans. Am. Math. Soc., to appear.
Bartle, R. G., andL. M. Graves: Mappings between function spaces. Trans. Am. Math. Soc.72, 400–413 (1952).
Bessaga, C., andV. Klee: Two topological properties of topological linear spaces. Israel J. Math.2, 211–220 (1964).
—— andA. Pełczyński: Some remarks on homeomorphisms ofF-spaces. Bull. Acad. Polon. Sci., Sér. sci. math. astr. et phys.10, 265–270 (1962).
Corson, H., andV. Klee: Topological classification of convex sets. Proc. Symp. Pure Math.7. — Convexity. Am. Math. Soc., Providence, R.I., 1963, 37–51.
Eidelheit, M.: Zur Theorie der Systeme linearer Gleichungen. Studia Math.6, 139–148 (1936).
Klee, V.: Convex bodies and periodic homeomorphisms in Hilbert space. Trans. Am. Math. Soc.74, 10–43 (1953).
—— Some topological properties of convex sets. Trans. Am. Math. Soc.78, 30–45 (1955).
—— Topological equivalence of a Banach space with its unit cell. Bull. Am. Math. Soc.67, 286–290 (1961).
Kolmogoroff, A.: Zur Normierbarkeit eines allgemeinen topologischen Raumes. Studia Math.5, 29–33 (1934).
Michael, E.: Convex structures and continuous selections. Canad. J. Math.11, 556–575 (1959).
Anderson, R. D.: Hilbert space is homeomorphic to the countable infinite product of lines. Bull. Am. Math. Soc.72, to appear (1966).
Kadec, M. I.: Topological equivalence of all separable Banach spaces. (Russian.) Dokl. Akad. Nauk SSSR, to appear.
Author information
Authors and Affiliations
Additional information
ToGottfried Köthe on his sixtieth birthday
The research was conducted at the University of Washington in 1963 when the first author was visiting there. The work of both authors was supported in part by the National Science Foundation, U.S.A. (NSF-GP-378).
Rights and permissions
About this article
Cite this article
Bessaga, C., Klee, V. Every non-normable Frechet space is homeomorphic with all of its closed convex bodies. Math. Ann. 163, 161–166 (1966). https://doi.org/10.1007/BF02052848
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02052848