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

Dobrowolski, T.; Mogilski, J.

doi:10.1090/S0002-9939-1982-0660623-0

Sigma-compact locally convex metric linear spaces universal for compacta are homeomorphic
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by T. Dobrowolski and J. Mogilski

Proc. Amer. Math. Soc. 85 (1982), 653-658

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

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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 ${l_2}$.

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