Feighn, Mark E. Separation properties of codimension-1 immersions. (English) Zbl 0658.57019 Topology 27, No. 3, 319-321 (1988). 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. Reviewer: F.Gomez Cited in 4 ReviewsCited in 8 Documents MSC: 57R42 Immersions in differential topology 55M05 Duality in algebraic topology Keywords:proper immersion; separation property; immersions of codimension 1 PDFBibTeX XMLCite \textit{M. E. Feighn}, Topology 27, No. 3, 319--321 (1988; Zbl 0658.57019) Full Text: DOI