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Proceedings of the American Mathematical Society

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Homotopically non-trivial
additive subgroups of Hilbert spaces


Author: Janusz Grabowski
Journal: Proc. Amer. Math. Soc. 127 (1999), 1563-1565
MSC (1991): Primary 46B25, 54F45, 20F26, 22A05
Published electronically: January 29, 1999
MathSciNet review: 1653394
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [Ca] Cauty, R.; Un exemple de sous-groupe additif de l'espace de Hilbert, Colloq. Math. 77 (1998), 147-162. CMP 98:12
  • [DG] Tadeusz Dobrowolski and Janusz Grabowski, Subgroups of Hilbert spaces, Math. Z. 211 (1992), no. 4, 657–669. MR 1191103, 10.1007/BF02571453
  • [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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Additional Information

Janusz Grabowski
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
Email: jagrab@mimuw.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-99-05245-4
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
Article copyright: © Copyright 1999 American Mathematical Society