Smale's degree for proper Fredholm maps

Summary

Smale's degree is a mod $2$ degree for proper Fredholm maps of index $0$ between connected Banach manifolds. It counts the preimages of a regular value modulo $2$. It extends the mod $2$ degree of a continuous map between compact manifolds of the same dimension to infinite dimensions. It rests on the Sard–Smale theorem, which supplies regular values.