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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sigma-compact locally convex metric linear spaces universal for compacta are homeomorphic


Authors: T. Dobrowolski and J. Mogilski
Journal: Proc. Amer. Math. Soc. 85 (1982), 653-658
MSC: Primary 57N17; Secondary 46A15, 57N20
MathSciNet review: 660623
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Abstract: 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}$.


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

  • [1] R. D. Anderson, On sigma-compact subsets of infinite-dimensional manifolds, Louisiana State Univ., preprint.
  • [2] 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 0273347 (42 #8227)
  • [3] -, Selected topics in infinite-dimensional topology, PWN, Warszawa, 1975.
  • [4] T. A. Chapman, Lectures on Hilbert cube manifolds, American Mathematical Society, Providence, R. I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975; Regional Conference Series in Mathematics, No. 28. MR 0423357 (54 #11336)
  • [5] 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 Loose Russian summary). MR 0264602 (41 #9194)
  • [6] -, $ (G - K)$-absorbing and skeletonized sets in metric spaces, Ph. D. Thesis, Inst. Math., Polish Acad. Sci., Warsaw, 1970.
  • [7] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of 𝑙₂-manifolds, Fund. Math. 101 (1978), no. 2, 93–110. MR 518344 (80g:57019)
  • [8] James E. West, The ambient homeomorphy of an incomplete subspace of infinite-dimensional Hilbert spaces, Pacific J. Math. 34 (1970), 257–267. MR 0277011 (43 #2748)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0660623-0
PII: S 0002-9939(1982)0660623-0
Keywords: $ \sigma $-compact linear span, linear space, topological embedding
Article copyright: © Copyright 1982 American Mathematical Society