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Homotopically non-trivial additive subgroups of Hilbert spaces

Author(s): Janusz Grabowski
Journal: Proc. Amer. Math. Soc. 127 (1999), 1563-1565.
MSC (1991): Primary 46B25, 54F45, 20F26, 22A05
Posted: January 29, 1999
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Abstract: We prove that for a line-free closed additive subgroup of a Hilbert space certain orthogonal projections lead to coverings of this group. This makes it possible to obtain additive subgroups which are homotopically non-trivial.

References:

[Ca]: Cauty, R.; Un exemple de sous-groupe additif de l'espace de Hilbert, Colloq. Math. 77 (1998), 147-162. CMP 98:12
[DG]: Dobrowolski, T. and Grabowski, J.; Subgroups of Hilbert spaces, Math. Z. 211 (1992), 657-669. MR 93k:58009
[We]: West, J.; Open problems in infinite dimensional topology, in Open Problems in Topology, J. van Mill and G. M. Reed editors, Elsevier, 1990, 524-597. CMP 91:03


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