Geodesic
An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes
Izvestiya. Mathematics , Tome 63 (1999) no. 6, pp. 1263-1273.

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An example is constructed of an infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes. 
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S. A. Shkarin. An infinite-dimensional separable pre-Hilbert space non-homeomorphic to any of its closed hyperplanes. Izvestiya. Mathematics , Tome 63 (1999) no. 6, pp. 1263-1273. http://geodesic.mathdoc.fr/item/IM2_1999_63_6_a6/

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