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Open mappings on spheres

Published online by Cambridge University Press:  09 April 2009

Edwin Duda
Edwin Duda
Affiliation:
University of Miami Coral Gables, Fla.
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In this paper we study open mappings of the sphere, Sn, onto itself. In particular, sufficient conditions are given that such a mapping be a homeomorphism. For the cases n≦ 2 many of the results could be obtained from the work of G. T. Whyburn [7], [8], and [10]. For the cases n ≦ 3 the useful results of A. V. Cernavskii, [1], [4], proved to be sufficient. An application is made concerning a finite to one open mapping of one n cell onto itself. It is interesting to note that for n ≦ 2 that we could use similar proofs to show that certain quasi-monotone mappings of Sn onto Sn are necessarily monotone mappings.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 330 - 334
Copyright
Copyright © Australian Mathematical Society 1969

References

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