Constructive decomposition of functions of two variables using functions of one variable

Details Constructive decomposition of functions of two variables using functions of one variable Constructive decomposition of functions of two variables using functions of one variable

2007-02-27

arxiv.org/abs/math/0702822v1

Mathematics

General Topology

Scientific paper

Given a compact set K in the plane, which contains no triple of points forming a vertical and a horizontal segment, and a continuous real-valued map f on K, we give a construction of real-valued continuous maps of one variable g,h such that f(x,y)=g(x)+h(y) for all points (x,y) from K. This provides a constructive proof of a part of Sternfeld's theorem on basic embeddings in the plane. In the proof we construct a sequence of finite graphs, which provide an arbitrarily good approximation of the set K.

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