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Maps with Discrete Branch Sets Between Manifolds of Codimension One

Published online by Cambridge University Press:  20 November 2018

J. G. Timourian
J. G. Timourian*
Affiliation:
Syracuse University, Syracuse, New York; University of Tennessee, Knoxville, Tennessee
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Let M n and Np be separable manifolds of dimensions n and p, respectively, with n ≧ p, and without boundary unless otherwise indicated. A mapƒ: M → N is proper if, for each compact set K ⊂ N, f –l(K) is compact. It is topologically equivalent to g: X → Y if there exist homeomorphisms α of M onto X and β of N onto Y such that βƒα–1 = g. At x ∈ M, ƒ is locally topologically equivalent to g if, for every neighbourhood W ⊂ M of x, there exist neighbourhoods U ⊂ W of x and V of ƒ(x) such that ƒ | U: U → V is topologically equivalent to g.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 660 - 668
Copyright
Copyright © Canadian Mathematical Society 1969

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