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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?)

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Keywords: <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img3.gif" ALT="$\sigma$">-compact linear span, linear space, topological embedding
Article copyright: © Copyright 1982 American Mathematical Society