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 $f\in C(K)$, wegive 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 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.
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机译：给定平面中的紧定集合$ K $，其中不包含形成垂直和水平线段的任何三点，并提供地图$ f \ in C（K）$，则构造函数$ g，h \ in C（\ mathbb R）$，使得K中所有$（x，y）\ f（x，y）= g（x）+ h（y）$。这提供了Sternfeld定理关于平面基本嵌入的一部分的建设性证明。在我们的证明中，集合$ K $由一组有限的点近似。
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