Authors: Cabello Sanchez, Felix, UEx, Badajoz 06071, Spain (fcabello@unex.es), and Cabello Sanchez, Javier, UEx, Badajoz 06071, Spain (coco@unex.es)
Nonlinear isomorphisms of lattices of Lipschitz functions, pp. 181-202.
ABSTRACTThe paper contains a number of Banach-Stone type theorems for lattices of uniformly continuous and Lipschitz functions without any linearity assumption. Sample result: two complete metric spaces of finite diameter are Lipschitz homeomorphic if (and only if, of course) the corresponding lattices of Lipschitz functions are isomorphic. Here, a lattice isomorphism is just a bijection preserving the order in both directions, in particular linearity is not assumed.