TRANSVERSAL NON-SUBSTITUTION THEOREMS

Abstract

The mathematical transversality in this paper yields Economically transversal non-substitution theorems for technology and market development level in which any non-transversal technology vectors remain unpriced. This result implies imports and exports to be complements, not substitutes. These theorems are reached by giving a uniquely path-lifting universal covering space for a Riesz kernel-like property for unique price functions to construct a global regular-valued equilibrium manifold. The universal covering formulation is justified through invariance of domain and dimension, and Borsuk-Ulam in the argument of a trivial fundamental group that enables a Sard-like transversality. A theorem is also given for a transversal measure space for the equilibrium proof using Dirac measure.