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Separation properties of codimension-1 immersions. (English) Zbl 0658.57019

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

MSC:

57R42 Immersions in differential topology
55M05 Duality in algebraic topology
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