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Proceedings of the American Mathematical Society

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

 

 

On atriodic tree-like continua


Authors: Lex G. Oversteegen and E. D. Tymchatyn
Journal: Proc. Amer. Math. Soc. 83 (1981), 201-204
MSC: Primary 54F20; Secondary 54B20, 54F50, 54H25
MathSciNet review: 620013
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Abstract: D. P. Bellamy has recently shown that atriodic tree-like continua do not have the fixed point property for homeomorphisms. J. B. Fugate and T. B. McLean showed that hereditarily indecomposable tree-like continua have the fixed point property for pointwise periodic homeomorphisms. In this paper the latter result is extended to the case of atriodic tree-like continua. In the course of the proof it is shown that the property of being an atriodic tree-like continuum is a Whitney property. In particular, it is shown that the hyperspace of an atriodic tree-like continuum is at most $ 2$-dimensional.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0620013-2
Keywords: Atriodic tree-like continua, pointwise periodic homeomorphism, fixed points, Whitney property
Article copyright: © Copyright 1981 American Mathematical Society