Geodesic
Topological proofs of Keller's theorem and an equivariant version of it
Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 621-629

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The known proofs of Keller's theorem that any infinite-dimensional compact convex set in Hilbert space is homeomorphic to the Hilbert cube are analytic. Here a topological proof of this theorem is given. A new approach to the old theorem leads to a proof of an equivariant version of Keller's theorem. 
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     author = {S. M. Ageev},
     title = {Topological proofs of {Keller's} theorem and an equivariant version of it},
     journal = {Izvestiya. Mathematics },
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     number = {3},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a7/}
}
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S. M. Ageev. Topological proofs of Keller's theorem and an equivariant version of it. Izvestiya. Mathematics , Tome 42 (1994) no. 3, pp. 621-629. http://geodesic.mathdoc.fr/item/IM2_1994_42_3_a7/