J. Korean Math. Soc. 2009; 46(3): 463-473
Printed May 1, 2009
https://doi.org/10.4134/JKMS.2009.46.3.463
Copyright © The Korean Mathematical Society.
Jos\'e Mar\'ia Soriano Arbizu
Universidad de Sevilla
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
2008; 45(2): 527-535
2022; 59(3): 495-517
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd