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Finitely Cyclic Homogeneous Continua

1991
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Proceedings of the American Mathematical Society
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A curve is finitely cyclic if and only if it is the inverse limit of graphs of genus < 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. A continuum is a compact, connected, nonvoid

doi:10.2307/2048797
fatcat:gwlm6p7kdfdwjh3yapgn7tpgqy