Journal of the
Korean Mathematical Society JKMS

Sufficient conditions are given to assert that between any two Banach spaces over $\mathbb K$ Fredholm mappings share exactly $N$ values in a specific open ball. The proof of the result is constructive and is based upon continuation methods.

Keywords: zero point, continuation methods, continuous dependence theorem, $C^1$-homotopy, proper mapping, compact mapping, regular value, Fredholm mapping, isomorphism

MSC numbers: Primary 58C30; Secondary 65H10