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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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/

[1] Keller O. H., “Die Homoimorpfis der Kompakten konvehen Mengen in Hilbertschen Raum”, Math. Ann., 105 (1931), 748–758 | DOI | MR | Zbl

[2] Bessaga C., Pelczynski A., Selected topics in infinite-dimensional topology, Warszawa, 1975 | MR | Zbl

[3] Dobrowolski T., Torunczyk H., “On metric linear spaces homeomorfic to $l_2$ and compact convex sets homeomorfic to $Q$”, Bull. Acad. Polon. Sci., 27 (1979), 883–887 | MR | Zbl

[4] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[5] Barut A., Ronchka P., Teoriya predstavlenii grupp i ee prilozhenii, t. 1, Mir, M., 1980 | Zbl

[6] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR

[7] Ageev S. M., “Klassifikatsiya $G$-prostranstv”, Izv. RAN. Ser. matem., 56:6 (1992), 1345–1357 | MR | Zbl

[8] Aleksandrov P. S., Pasynkov B. A., Vvedenie v teoriyu razmernosti, Nauka, M., 1973 | MR

[9] Rurk K., Sanderson B., Vvedenie v kusochno lineinuyu topologiyu, Mir, M., 1974 | MR