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 -compact locally convex metric linear space containing a topological copy of the Hilbert cube is homeomorphic to the linear span of the Hilbert cube , in the Hilbert space .

**[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****[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****[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****[6]**-,*-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****[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**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0660623-0

Keywords:
-compact linear span,
linear space,
topological embedding

Article copyright:
© Copyright 1982
American Mathematical Society