The free abelian topological group and the free locally convex space on the unit interval

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dc.creatorLeiderman, A. G.
dc.creatorMorris, S. A.
dc.creatorPestov, V. G.
dc.date1992-12-11
dc.date.accessioned2026-07-07T09:13:22Z
dc.date.available2026-07-07T09:13:22Z
dc.descriptionWe give a complete description of the topological spaces $X$ such that the free abelian topological group $A(X)$ embeds into the free abelian topological group $A(I)$ of the closed unit interval. In particular, the free abelian topological group $A(X)$ of any finite-dimensional compact metrizable space $X$ embeds into $A(I)$. The situation turns out to be somewhat different for free locally convex spaces. Some results for the spaces of continuous functions with the pointwise topology are also obtained. Proofs are based on the classical Kolmogorov's Superposition Theorem.
dc.description10 pages, AmS TeX 2.1
dc.identifierhttps://arxiv.org/abs/funct-an/9212001
dc.identifierhttp://arxiv.org/abs/funct-an/9212001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152303
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.titleThe free abelian topological group and the free locally convex space on the unit interval
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