Separation properties of codimension-1 immersions
type: Item
instance of: scholarly article
title: Separation properties of codimension-1 immersions
zbMATH Open document ID: 0658.57019
DOI: 10.1016/0040-9383(88)90013-4
author: Mark Feighn
published in: Topology
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 55M05
zbMATH DE Number: 4076085
zbMATH Keywords: proper immersion
zbMATH Keywords: separation property
zbMATH Keywords: immersions of codimension 1
reviewed by: Francisco Gómez
MaRDI profile type: Publication
full work available at URL: 0040-9383(88)90013-4
OpenAlex ID: W2063374152
description: scientific article; zbMATH DE number 4076085