Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-01T00:32:30.892Z Has data issue: false hasContentIssue false
  • English
  • Français

THE FREE ABELIAN TOPOLOGICAL GROUP AND THE FREE LOCALLY CONVEX SPACE ON THE UNIT INTERVAL

Published online by Cambridge University Press:  01 December 1997

ARKADY LEIDERMAN ,
SIDNEY A. MORRIS  and
VLADIMIR PESTOV
ARKADY LEIDERMAN
Affiliation:
Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, Israel
SIDNEY A. MORRIS
Affiliation:
University of South Australia, City West Campus, North Terrace, Adelaide, South Australia 5000, Australia
VLADIMIR PESTOV
Affiliation:
Victoria University of Wellington, P.O. Box 600, Wellington, New Zealand
Get access

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 529 - 538
Copyright
The London Mathematical Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)