On the mapping intersection problem

Alexander Dranishnikov

Vol. 173 (1996), No. 2, 403–412

DOI: 10.2140/pjm.1996.173.403

Abstract

It is proved that if the inequality dimX × Y < n holds for compacta X and Y with dimX or dimY ≠n − 2 then for every pair of maps f : X → ℝⁿ and g : Y → ℝⁿ and for any 𝜖 > 0 there are 𝜖-close maps f′ : X → ℝⁿ and g′ : Y → ℝⁿ with f′(X) ∩ g′(Y ) = ⊘. 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.

Mathematical Subject Classification 2000

Primary: 54F45

Secondary: 54C99, 55M10

Milestones

Received: 27 April 1993

Revised: 14 March 1994

Published: 1 April 1996