This Is a Review, Prepared for Ieee Control Systems, of Implicit Functions and Solution Mappings: a View from Variational Analysis, by Asen L. Dontchev, and R. Tyrrell Rockafellar. It Appeared in Springer Monographs

When I was first introduced to inverse and implicit functions as an undergraduate in the late sixties, students were drilled in the need to have functions as a prerequisite to doing analysis. Multivalued relations were to be avoided as much as possible. Indeed, Claude Berge’s influential book [2] doing elementary point-set topology with multifunctions first appeared in English — finely translated by my father’s St Andrew’s topologist colleague — in 1963 and was largely ignored. It is still in print despite Frank Bonsall’s review [4]: