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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.
  • C. Bessaga and A. Pełczyński, The estimated extension theorem, homogeneous collections and skeletons, and their applications to the topological classification of linear metric spaces and convex sets, Fund. Math. 69 (1970), 153–190. MR 273347, DOI 10.4064/fm-69-2-153-190
  • —, Selected topics in infinite-dimensional topology, PWN, Warszawa, 1975.
  • T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357
  • H. Toruńczyk, Skeletonized sets in complete metric spaces and homeomorphisms of the Hilbert cube, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 119–126 (English, with Russian summary). MR 264602
  • —, $(G - K)$-absorbing and skeletonized sets in metric spaces, Ph. D. Thesis, Inst. Math., Polish Acad. Sci., Warsaw, 1970.
  • H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of $l_{2}$-manifolds, Fund. Math. 101 (1978), no. 2, 93–110. MR 518344, DOI 10.4064/fm-101-2-93-110
  • 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