The implicit function theorem for continuous functions

Carlos Biasi, Carlos Gutierrez, Edivaldo L. dos Santos

DOI: http://dx.doi.org/10.12775/TMNA.2008.044

Abstract


In the present paper we obtain a new homological version of the
implicit function theorem and some versions of the Darboux theorem.
Such results are proved for continuous maps on topological
manifolds. As a consequence, some versions of these classic theorems
are proved when we consider differenciable (not necessarily $C^{1}$)
maps.

Keywords


Darboux theorem; implicit function theorem; differentiable maps; degree of a map

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