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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A two-color theorem for analytic maps in $ {\bf R}\sp{n}$


Author: Bryan E. Cain
Journal: Proc. Amer. Math. Soc. 39 (1973), 261-266
MSC: Primary 05C15; Secondary 55A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0317981-0
MathSciNet review: 0317981
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Abstract: $ {f_1}, \cdots ,{f_k}$ are real analytic functions on $ {R^n}$ th then the connected components of $ {R^n}\backslash [f_1^{ - 1}(0) \cup \cdots \cup f_k^{ - 1}(0)]$ can be ``colored'' with two colors so that two components will have different colors whenever their common boundary contains a topological $ (n - 1)$-manifold.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0317981-0
Article copyright: © Copyright 1973 American Mathematical Society