Subtraction Theorems and Approximate Openness for Multifunctions: Topological and Infinitesimal Viewpoints

An approximate open mapping principle for multifunctions between metric spaces with closed graphs is given. It is shown that infinitesimal assumptions involving tangent cones and approximate tangent cones ensure that openness results can be derived from the general principle. Several examples and counterexamples enlight the validity and the interplay of the results. Applications are given to the lower semicontinuity of the intersection of two multifunctions.