Journal of the
Korean Mathematical Society JKMS

Two $C^{1}$-mappings, whose domain is a connected compact $C^{1}$-Banach manifold modelled over a Banach space $X$ over $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$ and whose range is a Banach space $Y$ over $\mathbb{K},$ are introduced. Sufficient conditions are given to assert they share only a value. The proof of the result, which is based upon continuation methods, is constructive.

Keywords: regular value, continuation methods, atlas, chart, Banach manifold, compactness

MSC numbers: Primary 58C30, Secondary 65H20