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

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

1992-12-11

arxiv.org/abs/funct-an/9212001v1

Mathematics

Operator Algebras

10 pages, AmS TeX 2.1

Scientific paper

We 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.

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