A criterion for Banach manifolds with a separable model to be finite-dimensional - Savkin, V. I. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
We give an example of a continuous bijective mapping with a discontinuous inverse which acts in a separable Banach space and differs from the identical mapping only in an open unit ball. A criterion for Banach manifolds with a separable model to be finite-dimensional is established in terms of the continuity of inverse operators.