Positivity

, Volume 6, Issue 3, pp 243–260

Euler Characteristic and Fixed-Point Theorems

Authors

  • B. Cornet
    • CERMSEM, Maison des Sciences EconomiquesUniversité Paris 1
Article

DOI: 10.1023/A:1020242731195

Cite this article as:
Cornet, B. Positivity (2002) 6: 243. doi:10.1023/A:1020242731195

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.

Euler characteristicFixed-pointNormal and tangent cones
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© Kluwer Academic Publishers 2002