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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Constructive decomposition of a function of two variables as a sum of functions of one variable
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by Eva Miliczká PDF
Proc. Amer. Math. Soc. 137 (2009), 607-614 Request permission

Abstract:

Given a compact set $K$ in the plane, which does not contain any triple of points forming a vertical and a horizontal segment, and a map $f\in C(K)$, we give a construction of functions $g,h\in C(\mathbb R)$ such that $f(x,y)=g(x)+h(y)$ for all $(x,y)\in K$. This provides a constructive proof for a part of Sternfeld’s theorem on basic embeddings in the plane. In our proof the set $K$ is approximated by a finite set of points.
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Additional Information
  • Eva Miliczká
  • Affiliation: Institute of Computer Science, Faculty of Science, P. J. Šafárik University, Jesenná 5, 040 01 Košice, Slovakia
  • Email: eva.miliczka@upjs.sk
  • Received by editor(s): January 16, 2007
  • Received by editor(s) in revised form: January 31, 2008
  • Published electronically: August 27, 2008
  • Additional Notes: The author was supported by grants VEGA 1/3002/06 and VEGA 1/3128/06
  • Communicated by: Alexander N. Dranishnikov
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 607-614
  • MSC (2000): Primary 26B40, 54C30; Secondary 54F99, 54C25
  • DOI: https://doi.org/10.1090/S0002-9939-08-09528-2
  • MathSciNet review: 2448582