Fréchet manifold
topological space modeled on a Fréchet space in much the same way as a manifold is modeled on a Euclidean space
string group
topological group, not presentable as a finite-dimensional Lie group, but presentable as a Frechet Lie group, obtained by killing the third homotopy group of the spin group
Banach manifold
manifold modeled on Banach spaces; topological space in which each point has a neighbourhood homeomorphic to an open set in a Banach space