On a problem of G. G. Lorentz

Let C(B) denote the space of real-valued continuous functions on B. At the conference "Harmonic Analysis and Approximations" held at Nor Amberd in Armenia in September, 1998, the following general problem was posed by Professor George G. Lorentz: Find conditions on finite-dimensional subspaces U and V so that U/V is a uniqueness set in the problem of best uniform approximation to elements of C(B). In this paper we consider this problem. (C) 2000 Academic Press.