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

Arkady Leiderman, Sidney A. Morris, Vladimir Pestov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

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) on the closed unit interval. In particular, the free abelian topological group A(X) on any finite-dimensional compact metrizable space X embeds into A(I). To obtain our description, we study similar embeddings of the free locally convex spaces and continuous surjections between the spaces of continuous functions with the pointwise topology. Proofs are based on the classical Kolmogorov's Superposition Theorem.

Original languageEnglish
Pages (from-to)529-538
Number of pages10
JournalJournal of the London Mathematical Society
Volume56
Issue number3
DOIs
StatePublished - 1 Jan 1997

ASJC Scopus subject areas

  • Mathematics (all)

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