On the gluing of hyperconvex metrics and diversities

Abstract

In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) $(X, δ_x)$ and $(Y, δ_y)$ with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.