The free abelian topological group and the free locally convex space on the unit interval
Abstract
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 finitedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 December 1992
 arXiv:
 arXiv:functan/9212001
 Bibcode:
 1992funct.an.12001L
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Operator Algebras
 EPrint:
 10 pages, AmS TeX 2.1