## Constructive decomposition of a function of two variables as a sum of functions of one variable

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- by Eva Miliczká
- Proc. Amer. Math. Soc.
**137**(2009), 607-614 - DOI: https://doi.org/10.1090/S0002-9939-08-09528-2
- Published electronically: August 27, 2008
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## 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.## References

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## Bibliographic 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