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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed points for confluent maps onto disks


Author: Sam B. Nadler
Journal: Proc. Amer. Math. Soc. 78 (1980), 116-118
MSC: Primary 54H25; Secondary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1980-0548096-8
MathSciNet review: 548096
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Abstract: Let M be a compact subset of a disk D such that $ {H^1}(M) \approx 0$. It is shown that if f is a confluent mapping from M onto D and if g is any mapping from M into D, then $ f(p) = g(p)$ for some $ p \in M$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0548096-8
Keywords: Confluent map, essential map, fixed point, monotone map, open map, quasi-interior map, universal map
Article copyright: © Copyright 1980 American Mathematical Society