Nonexpansive Retractions in Hyperconvex Spaces

This paper is primarily concerned with the study of conditions on a hyperconvex subset D of a hyperconvex metric space M which assure that there exists a nonexpansive retraction R of M\D onto D which has the property that R M\D ⊂ ∂D A related question we take up is, when is such a retraction R proximinal, that is, when does R have the property d x R x = dist x D 1Most of this research was conducted while the first author was visiting the University of Iowa. He thanks the faculty and staff of the Mathematics Department at Iowa for their kind hospitality. Also, the first and third authors acknowledge the support of DGICYT Research Project PB96-1338-C02-01.