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The Free Abelian Topological Group and the Free Locally Convex Space on the Unit Interval
Author(s) -
Leiderman Arkady,
Morris Sidney A.,
Pestov Vladimir
Publication year - 1997
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610797005577
Subject(s) - mathematics , abelian group , locally convex topological vector space , topological group , unit interval , topological ring , topological vector space , metrization theorem , topology (electrical circuits) , group (periodic table) , topological space , topological algebra , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , physics , quantum mechanics , separable space
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.