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Topological structure of non-separable sigma-locally compact convex sets

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 نشر من قبل Taras Banakh
 تاريخ النشر 2013
  مجال البحث
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For an infinite cardinal $kappa$ let $ell_2(kappa)$ be the linear hull of the standard othonormal base of the Hilbert space $ell_2(kappa)$ of density $kappa$. We prove that a non-separable convex subset $X$ of density $kappa$ in a locally convex linear metric space if homeomorphic to the space (i) $ell_2^f(kappa)$ if and only if $X$ can be written as countable union of finite-dimensional locally compact subspaces, (ii) $[0,1]^omegatimes ell_2^f(kappa)$ if and only if $X$ contains a topological copy of the Hilbert cube and $X$ can be written as a countable union of locally compact subspaces.



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