# Constructive decomposition of a function of two variables as a sum of functions of one variable - Mathematics > General Topology

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Abstract: Given a compact set $K$ in the plane, which does not contain any triple ofpoints forming a vertical and a horizontal segment, and a map $f\in CK$, wegive a construction of functions $g,h\in C\mathbb R$ such that$fx,y=gx+hy$ for all $x,y\in K$. This provides a constructive proof ofa part of Sternfeld-s theorem on basic embeddings in the plane. In our proofthe set $K$ is approximated by a finite set of points.

Author: ** Eva Trenklerová**

Source: https://arxiv.org/