The main purpose of this paper is to outline that the definable Debreu map is a local definable diffeomorphism. It implies the equilibrium is locally determined in each connected component partitioning a regular O-minimal equilibrium manifold. It complements the result in Theorem 5 of Arias-R....

The main purpose of this paper is to remark that any definable continuous path linking two regular equilibria in a regular O-minimal equilibrium manifold intersects a finite number of definable connected components locally determined. We apply the cell decomposition theorem to decompose the...