FREDHOLM MAPPINGS AND BANACH MANIFOLDS

Abstract

Two C 1 -mappings, whose domain is a connected compact C 1 -Banach manifold modelled over a Banach space X over K = R or C and whose range is a Banach space Y over K; are introduced. Su-cient conditions are given to assert they share only a value. The proof of the result, which is based upon continuation methods, is constructive. 1. Preliminaries Scientiflc phenomena are locally described by parameters, whose choice is sometimes arbitrary. This implies the importance of the availability of a methodology for the comparison of results of measurements. Locally, a Banach manifold looks like a Banach space. For a local description, difierent Banach (or coordinate or parameter) spaces are allowed and transformation rules exist for these coordinates. Let X;Y be two Banach spaces. Let u : U ‰ X ! Y be a continuous mapping. One way of solving the equation (1) u(x) = y