Abstract
We propose a geometric definition of the Euler characteristic χ(M) for the class of compact epi-Lipschitzian sets M⊂Rn and we provide existence theorems of (generalized) equilibria for set-valued mappings F when the domain M of F is neither assumed to be convex, nor smooth but has a nonzero Euler characteristic.
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Cornet, B. Euler Characteristic and Fixed-Point Theorems. Positivity 6, 243–260 (2002). https://doi.org/10.1023/A:1020242731195
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DOI: https://doi.org/10.1023/A:1020242731195