Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F15, 54F20

Retrieve articles in all journals with MSC: 54F15, 54F20

Additional Information

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

American Mathematical Society