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

 

Simply cyclic homogeneous non-tree-like curves decompose to solenoids


Author: James T. Rogers
Journal: Proc. Amer. Math. Soc. 108 (1990), 1059-1062
MSC: Primary 54F20; Secondary 54F50
MathSciNet review: 1002164
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Abstract: It is proved that if a one-dimensional, cyclic, homogeneous continuum $ X$ is the inverse limit of graphs each of which contains only one cycle, then $ X$ is a solenoid or $ X$ admits a decomposition into mutually homeomorphic, homogeneous, tree-like continua with quotient space a solenoid.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1002164-1
PII: S 0002-9939(1990)1002164-1
Keywords: Continuum, curve, homogeneous, terminal subcontinuum, decomposition, simply cyclic
Article copyright: © Copyright 1990 American Mathematical Society