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Ukrainian Mathematical Journal

, Volume 57, Issue 4, pp 666–670 | Cite as

Multiplicity of Continuous Mappings of Domains

  • Yu. B. Zelinskii
Brief Communications

Abstract

We prove that either the proper mapping of a domain of an n-dimensional manifold onto a domain of another n-dimensional manifold of degree k is an interior mapping or there exists a point in the image that has at least |k|+2 preimages. If the restriction of f to the interior of the domain is a zero-dimensional mapping, then, in the second case, the set of points of the image that have at least |k|+2 preimages contains a subset of total dimension n. In addition, we construct an example of a mapping of a two-dimensional domain that is homeomorphic at the boundary and zero-dimensional, has infinite multiplicity, and is such that its restriction to a sufficiently large part of the branch set is a homeomorphism.

Keywords

Continuous Mapping Proper Mapping Total Dimension Interior Mapping Infinite Multiplicity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yu. B. Zelinskii
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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