### The implicit function theorem for continuous functions

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.

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

#### Full Text:

FULL TEXT### Refbacks

- There are currently no refbacks.