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On the domain of implicit functions in a projective limit setting without additional norm estimates

Magnot Jean-Pierre

Demonstratio Mathematica

2020

Vol. 53, nr 1

112--120

We examine how implicit functions on ILB-Fréchet spaces can be obtained without metric or norm estimates which are classically assumed. We obtain implicit functions defined on a domain D which is not necessarily open, but which contains the unit open ball of a Banach space. The corresponding inverse function theorem is obtained, and we finish with an open question on the adequate (generalized) notion of differentiation, needed for the corresponding version of the Fröbenius theorem.