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http://dx.doi.org/10.4134/JKMS.2009.46.3.463

FREDHOLM MAPPINGS AND BANACH MANIFOLDS  

Arbizu, Jose Mara Soriano (DEPARTAMENTO DE ANALISIS MATEMATICO, FACULTAD DE MATEMATICAS UNIVERSIDAD DE SEVILLA)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.3, 2009 , pp. 463-473 More about this Journal
Abstract
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;
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