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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sigma-compact locally convex metric linear spaces universal for compacta are homeomorphic
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by T. Dobrowolski and J. Mogilski PDF
Proc. Amer. Math. Soc. 85 (1982), 653-658 Request permission


It is proved that every $\sigma$-compact locally convex metric linear space containing a topological copy of the Hilbert cube $Q$ is homeomorphic to $\Sigma$ the linear span of the Hilbert cube $Q$, in the Hilbert space ${l_2}$.
    R. D. Anderson, On sigma-compact subsets of infinite-dimensional manifolds, Louisiana State Univ., preprint.
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  • James E. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970), 257–267. MR 277011
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 85 (1982), 653-658
  • MSC: Primary 57N17; Secondary 46A15, 57N20
  • DOI:
  • MathSciNet review: 660623