Any infinite-dimensional Fréchet space homeomorphic with its countable product is topologically a Hilbert space

Terry, Wesley E.

doi:10.1090/S0002-9947-1974-0356065-8

Any infinite-dimensional Fréchet space homeomorphic with its countable product is topologically a Hilbert space
HTML articles powered by AMS MathViewer

by Wesley E. Terry PDF

Trans. Amer. Math. Soc. 196 (1974), 93-104 Request permission

Abstract:

In this paper we will prove that any infinite-dimensional Fréchet space homeomorphic with its own countable product is topologically a Hilbert space. This will be done in two parts. First we will prove the result for infinite-dimensional Banach spaces, and then we will show that the result for Fréchet spaces follows as a corollary.

References

C. Bessaga, On topological classification of complete linear metric spaces, Fund. Math. 56 (1964/65), 251–288. MR 178322, DOI 10.4064/fm-56-3-250-288
T. A. Chapman, Deficiency in infinite-dimensional manifolds, General Topology and Appl. 1 (1971), 263–272. MR 322898, DOI 10.1016/0016-660X(71)90097-3
William H. Cutler, Negligible subsets of infinite-dimensional Fréchet manifolds, Proc. Amer. Math. Soc. 23 (1969), 668–675. MR 248883, DOI 10.1090/S0002-9939-1969-0248883-5
David W. Henderson, Stable classification of infinite-dimensional manifolds by homotopy-type, Invent. Math. 12 (1971), 48–56. MR 290413, DOI 10.1007/BF01389826
David W. Henderson, Corrections and extensions of two papers about infinite-dimensional manifolds, General Topology and Appl. 1 (1971), 321–327. MR 293677, DOI 10.1016/0016-660X(71)90004-3
Victor L. Klee Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10–43. MR 54850, DOI 10.1090/S0002-9947-1953-0054850-X
V. L. Klee Jr., A note on topological properties of normed linear spaces, Proc. Amer. Math. Soc. 7 (1956), 673–674. MR 78661, DOI 10.1090/S0002-9939-1956-0078661-2
V. L. Klee Jr., Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30–45. MR 69388, DOI 10.1090/S0002-9947-1955-0069388-5
K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751

Une remarque sur l’homéomorphie des champs fonctionels

1

Ernest Michael, Local properties of topological spaces, Duke Math. J. 21 (1954), 163–171. MR 62424
Wesley E. Terry, Conditions for a TVS to be homeomorphic with its countable product, Trans. Amer. Math. Soc. 190 (1974), 233–242. MR 338725, DOI 10.1090/S0002-9947-1974-0338725-8

Absolute retracts as factors of normed linear spaces

G, K

absorbing and skeletonized sets in metric spaces