Separation properties of codimension-1 immersions
The author proves the following theorem: Let f: \(M^{n-1}\to N^ n\) be a proper \(C^ 2\)-immersion. Suppose \(H_ 1(N;Z/2Z)=0\). Then N-f(M) is not connected. In particular one has that any smooth immersion of \(S^ 2\) in \(R^ 3\) separates \(R^ 3\) into at least two components.
scientific article; zbMATH DE number 4076085