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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

No homogeneous tree-like continuum contains an arc


Author: Charles L. Hagopian
Journal: Proc. Amer. Math. Soc. 88 (1983), 560-564
MSC: Primary 54F15; Secondary 54F20
MathSciNet review: 699434
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Abstract: In 1960 R. H. Bing [4, p. 210] asked the following question. "Is there a homogeneous tree-like continuum that contains an arc?" We answer this question in the negative. This result generalizes Bing's theorem [4, p. 229] that every atriodic homogeneous tree-like continuum is arcless.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699434-X
PII: S 0002-9939(1983)0699434-X
Keywords: Homogeneity, tree-like continuum, arcless continuum, tree chain, hereditarily indecomposable continuum, pseudo-arc, dog-chases-rabbit principle
Article copyright: © Copyright 1983 American Mathematical Society