A two-color theorem for analytic maps in $\textbf {R}^{n}$
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- by Bryan E. Cain PDF
- Proc. Amer. Math. Soc. 39 (1973), 261-266 Request permission
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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- 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