Density of extremal sets in multivariate Chebyshev approximation (Q1867516)

There are numerous results concerning the density of extremal sets (points of maximal deviation) in univariate Chebyshev approximation. An example given in the paper shows that density may occur just in ``one of the coordinates'', and the author verifies that this ``weak density'' holds in general, in case of bivariate approximation on the square. It is also remarked that the case of approximation on a \(d\)-dimensional cube is similar.