The topological space of Schur-concave copulas is homeomorphic to the Hilbert cube (Q6571158)

Schur-concave ccopulas were introduced in [\textit{F. Durante} and \textit{C. Sempi}, Int. Math. J. 3, No. 9, 893--905 (2003; Zbl 1231.60014)], see the book [\textit{A. W. Marshall} and \textit{I. Olkin}, Inequalities: theory of majorization and its applications. New York etc.: Academic Press (1979; Zbl 0437.26007)] for the definition of Schur-concavity. It is known that the subset \(C_{SC}\) of Schur-concave copulas is compact in the topology of uniform convergence. The main result of this paper is that \(C_{SC}\) is homeomorphic to the Hilbert cube, and, as a consequence, has the fixed point property. The methods used in the proof are from infinite-dimensional topology.