References
Anderson, R. D.: Hilbert space is homeomorphic to the countable product of real lines. Bull. Amer. Math. Soc.72, 515–519 (1966).
Bessaga, C., Kadeč, M. I.: On topological classification of non-separable Banach spaces. Symposium on Infinite-dimensional Topology, Baton Rouge, La., 1967.
Eidelheit, M., Mazur, S.: Eine Bemerkung über die Räume vom Typus (F). Studia Math.7, 159–161 (1938).
Henderson, D. W.: Stable classification of infinite-dimensional manifolds by homotopy type (to appear).
—, Schori, R.: Topological classification of infinite-dimensional manifolds by homotopy type. Bulletin Amer. Math. Soc.76, 121–124 (1970).
Kelley, J. L., Namioka, I., et al.: Linear topological spaces. Princeton: Van Nostrand 1963.
Kister, J. M.: Microbundles are fibre bundles. Annals of Math.80, 190–199 (1964).
Kuiper, N. H., Lashof, R. K.: Microbundles and bundles, I. Inventiones Math.1, 1–17 (1966).
Renz, P. L.: The contractibility of the homeomorphism group of some product spaces by Wong's method. Math. Scand. (to appear).
Whitehead, H. C.: Combinatorial homotopy I. Bull. Amer. Math. Soc.55, 213–214 (1959).
Wong, R. Y. T.: On homeomorphisms of certain infinite dimensional spaces. Trans. Amer. Math. Soc.128, 148–154 (1967).
Bessaga, C., Klee, V.: Every non-normable Fréchet space is homeomorphic with all of its closed convex bodies. Mant. Ann.163, 161–166 (1966).
Dugundji, J.: Topology. Boston: Allyn and Bacon 1966.
Henderson, D. W.: Corrections and extensions of two papers about infinite-dimensional manifolds (to appear).
—, West, J. E.: Triangulated infinite-dimensional manifolds. Bulletin Amer. Math. Soc.76, 655–660 (1970).
Milnor, J.: Microbundles. Part I. Topology3, 53–80 (1964).
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The author is an Alfred P. Sloan Fellow and was partially supported by NSF grant GP93997. The author wishes to thank Douglas Curtiss and Czeslaw Bessaga for pointing out several errors in the original manuscript. Some revisions of this paper were carried out while the author was a guest at the Mathematical Institute of the Polish Academy of Sciences. The author wishes to thank the referee for some useful suggestions.
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Henderson, D.W. Micro-bundles with infinite-dimensional fibers are trivial. Invent Math 11, 293–303 (1970). https://doi.org/10.1007/BF01403183
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DOI: https://doi.org/10.1007/BF01403183