Uniform homeomorphisms between spheres induced by interpolation methods

M. Daher [9] showed that if $(X_0, X_1)$ is a regular couple of uniformly convex spaces then the unit spheres of the complex interpolation spaces $X_{\theta}$ and $X_{\eta}$ are uniformly homeomorphic for every $0 < \theta, \eta < 1$. We show that this is a rather general phenomenon of interpolation methods described by the discrete framework of interpolation of [15].