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Proceedings of the American Mathematical Society

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

 

 

A fixed point theorem for inverse limits of fans


Author: M. M. Marsh
Journal: Proc. Amer. Math. Soc. 91 (1984), 139-142
MSC: Primary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1984-0735580-0
MathSciNet review: 735580
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Abstract: In [1] David Bellamy gave an example of a tree-like continuum without the fixed point property. Another example of a tree-like continuum which admits a fixed point free mapping was given in [5] by L. G. Oversteegen and J. T. Rogers, Jr. We prove in this paper that a certain inverse limit of fans has the fixed point property. Certain possible methods for simplifying Bellamy's and Oversteegen and Roger's examples are eliminated by our theorem.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735580-0
Keywords: Inverse limit, fan, tree chain, fixed point property
Article copyright: © Copyright 1984 American Mathematical Society