A homological version of the implicit function theorem - Biasi, C.; dos Santos, E. L. (Springer, 2006)
Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.
Keywords: Implicit Function Theorem; topological monoids; topological groups; Lie groups; generalized manifolds