Counterexample to a Problem on Tensor Product Approximation Original Research Article

Answering a conjecture of M. von Golitschek in the negative, a compact setKis constructed on the plane such that not every continuous function onKcan be uniformly approximated by continuous functions of the formg(x)+h(y), and yetKdoes not contain a closed path of points with consequitive points connected with alternatively horizontal and vertical segments.