On sets admitting chebyshev vector systems

Abstract

We study the topological properties of compacta on which exist vector (with values in space Rs) systems of Chebyshev functions or systems having a given Chebyshev rank. The lengths of the systems are assumed to be multiples of but not equal to the number s. A compactum on which a Chebyshev system exists is embedded into space Rs. On polytopes of dimension s + 1 the Chebyshev ranks of vector systems grow to infinity together with their length.