More monotone open homogeneous locally connected plane continua

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This paper constructs a continuous decomposition of the Sierpiński curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpiński curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpiński curve and identifying two points on the boundary of one of its complementary domains. This outcome is shown to imply that there are continuum many topologically different one dimensional locally connected plane continua that are homogeneous with respect to monotone open maps.
22 pages, 9 figures, for AMS Contemporary Mathematics Series, "Geometry and Topology in Dynamics"

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Geometric Topology, General Topology, 54B15;54C10;54E45;54F50

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http://salesiana.dossiersoluciones.com/handle/123456789/78933

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9908042
 http://arxiv.org/abs/math/9908042

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arXiv