Convenient vector space

Summary

A convenient vector space is a locally convex space that is complete in a weak sense: every Mackey–Cauchy sequence converges. These spaces are the setting of the convenient calculus of Frölicher, Kriegl and Michor. In it, a map is smooth when it sends smooth curves to smooth curves. The category of convenient spaces and smooth maps is cartesian closed.

This makes spaces of smooth maps, and manifolds of mappings, easy to handle without Banach-space estimates.