Homotopically non-trivial additive subgroups of Hilbert spaces
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- by Janusz Grabowski PDF
- Proc. Amer. Math. Soc. 127 (1999), 1563-1565 Request permission
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
- Cauty, R.; Un exemple de sous-groupe additif de l’espace de Hilbert, Colloq. Math. 77 (1998), 147–162.
- Tadeusz Dobrowolski and Janusz Grabowski, Subgroups of Hilbert spaces, Math. Z. 211 (1992), no. 4, 657–669. MR 1191103, DOI 10.1007/BF02571453
- 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.
Additional Information
- Janusz Grabowski
- Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
- Email: jagrab@mimuw.edu.pl
- Received by editor(s): August 1, 1998
- Received by editor(s) in revised form: August 28, 1998
- Published electronically: January 29, 1999
- Additional Notes: Supported by KBN, grant No. 2 PO3A 042 10.
- Communicated by: Dale Alspach
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1563-1565
- MSC (1991): Primary 46B25, 54F45, 20F26, 22A05
- DOI: https://doi.org/10.1090/S0002-9939-99-05245-4
- MathSciNet review: 1653394