Ukrainian Mathematical Journal

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

Multiplicity of Continuous Mappings of Domains

  • Yu. B. Zelinskii
Brief Communications


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.


Continuous Mapping Proper Mapping Total Dimension Interior Mapping Infinite Multiplicity 
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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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