Uniform embeddings, homeomorphisms and quotient maps between Banach spaces (a short survey)

AbstractThe paper is a short survey dealing with questions of the following type: For which pair of Banach spaces X and Y is X Lipschitz equivalent or uniform homeomorphic to a subset of Y? To what extent does the uniform structure of a Banach space or its unit ball determine the linear structure of the space? What is the right notion of a nonlinear quotient space