The uniform structure of Banach spaces
نویسنده
چکیده
We explore the existence of uniformly continuous sections for quotient maps. Using this approach we are able to give a number of new examples in the theory of the uniform structure of Banach spaces. We show for example that there are two non-isomorphic separable L1-subspaces of 1 which are uniformly homeomorphic. We also prove the existence of two coarsely homeomorphic Banach spaces (i.e. with Lipschitz isomorphic nets) which are not uniformly homeomorphic (answering a question of Johnson, Lindenstrauss and Schechtman). We construct a closed subspace of L1 whose unit ball is not an absolute uniform retract (answering a question of the author).
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