Simply cyclic homogeneous non-tree-like curves decompose to solenoids. (English) Zbl 0688.54022
Summary: 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.
MSC:
| 54F15 | Continua and generalizations |
| 54F50 | Topological spaces of dimension \(\leq 1\); curves, dendrites |
Keywords:
one-dimensional, cyclic, homogeneous continuum; inverse limit of graphs; solenoid; decomposition; homogeneous, tree-like continuaReferences:
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