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Finitely cyclic homogeneous continua


Authors: Paweł Krupski and James T. Rogers
Journal: Proc. Amer. Math. Soc. 113 (1991), 1173-1177
MSC: Primary 54F15; Secondary 54F50
DOI: https://doi.org/10.1090/S0002-9939-1991-1062393-9
MathSciNet review: 1062393
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Abstract: A curve is finitely cyclic if and only if it is the inverse limit of graphs of genus $ \leq k$ , where $ k$ is some integer. In this paper it is shown that if $ X$ is a homogeneous finitely cyclic curve that is not tree-like, then $ X$ is a solenoid or $ X$ admits a decomposition into mutually homeomorphic, homogeneous, tree-like continua with quotient space a solenoid. Since the Menger curve is homogeneous, the restriction to finitely cyclic curves is essential.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1062393-9
Keywords: Continuum, curve, homogeneous, terminal subcontinuum, decomposition, simply cyclic, finitely cyclic
Article copyright: © Copyright 1991 American Mathematical Society

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