On the mapping intersection problem

Abstract

It is proved that if the inequality dimX x Y Rn and for any e > 0 there are e-close maps /' : X -> Rn and g' : Y -)> Rn with f'(X)Γ\g'(Y) = 0. Thus an affirmative answer to the Mapping Intersection Problem is given except in the codimension two case. The solution is based on previous results in this subject and on a generalization of the Eilenberg Theorem.