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Literature cited
K. Borsuk, “Concerning the set of retractions,” Colloq. Math.,18, 197–201 (1967).
T. A. Chapman, “The spaces of retractions of a compact Hilbert cube manifold is an ANR,” Topology Proc.,2, 409–430 (1977).
K. Sakai, “The space of retractions of a compact Q-manifold in an ℓ2.-manifold,” Proc. Am. Math. Soc.,83, No. 2, 421–424 (1981).
T. A. Chapman, Lectures on Q-manifolds [Russian translation], Mir, Moscow (1981).
H. Torunczyk, “Absolute retracts as factors of normal linear spaces,” Fund. Math.,86, No. 1, 53–67 (1974).
H. Torunczyk, “Characterizing Hilbert space topology,” Fund. Math.,111, No. 3, 247–262 (1981).
D. W. Henderson, “Infinite dimensional manifolds are open subsets of Hilbert spaces,” Topology,9, No. 1, 25–34 (1970).
U. O. Tashmetov, “Connectedness and local connectedness of hyperspaces,” Sib. Mat. Zh.,15, No. 5, 1115–1130 (1974).
M. Morse, “A special parametrization of curves,” Bull. Am. Math. Soc.,42, 915–922 (1936).
R. Geoghegan, “On spaces of homeomorphisms, embeddings and functions I,” Topology,11, No. 2, 159–177 (1972).
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Translated from Matematicheskie Zametki, Vol. 42, No. 1, pp. 94–100, July, 1987.
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Basmanov, V.N., Savchenko, A.G. Hilbert space as the space of retractions of an interval. Mathematical Notes of the Academy of Sciences of the USSR 42, 563–566 (1987). https://doi.org/10.1007/BF01138727
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DOI: https://doi.org/10.1007/BF01138727