Free topological vector spaces

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Gabriyelyan, Saak S.; Morris, Sidney A.;
  • Subject: Mathematics - General Topology | 46A03, 54A25, 54D50

We define and study the free topological vector space $\mathbb{V}(X)$ over a Tychonoff space $X$. We prove that $\mathbb{V}(X)$ is a $k_\omega$-space if and only if $X$ is a $k_\omega$-space. If $X$ is infinite, then $\mathbb{V}(X)$ contains a closed vector subspace whi... View more
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