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- Title
Open mappings on spheres.
- Authors
Duda, Edwin
- Abstract
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.
- Publication
Journal of the Australian Mathematical Society, 1969, Vol 10, Issue 3/4, p330
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788700007564