On the mapping intersection problem (Q1814765)

Two compacta \(X,Y\) have the unstable intersection property in Euclidean space \(\mathbb{R}^n\) \((X|Y)\) if any maps \(f:X \to\mathbb{R}^n\), \(g:Y\to\mathbb{R}^n\) can be approximated arbitrarily close by maps \(f'\), \(g'\) with disjoint images. The main theorem of the author asserts the equivalence of (1) \(\dim X\times Y<n\), (2) \(X|Y\) in \(\mathbb{R}^n\) if both compacta are not of dimension \(n-2\). This theorem extends results of D. McCullough and L. Rubin as well as those of the author himself.