Multiplicity of Continuous Mappings of Domains
AbstractWe 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.
How to Cite
ZelinskiiY. B. “Multiplicity of Continuous Mappings of Domains”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, no. 4, Apr. 2005, pp. 554–558, http://umj.imath.kiev.ua/index.php/umj/article/view/3620.