Une note sur un théorème de point-fixe.

We present a theorem on the existence of a maximal element for a correspondence which is upper hemi-continuous in some variables and which satisfies with respect to the other ones one the following conditions : (i) lower semi-continuous if the space has a finite dimension, (ii) lower semi-continuous if the space is complete, (iii) open fibers. This theorem generalizes the result of Gale-Mas-Colell (1975-1979) and the one of Bergstrom (1975) and extend to the infinite dimensional setting the result of Gourdel (1995).Fixed-point, maximal element, upper hemi-continuous, selection theorems, endogenous endowments.