Monotone preimages of dendrites |
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Authors: | Evan P. Wright |
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Affiliation: | Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY 11794, USA |
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Abstract: | A counterexample to a theorem of J.J. Charatonik and K. Omiljanowski giving sufficient conditions for a dendrite to be contained in all of its monotone preimages is given, and a corrected version of the theorem is presented. An alternative proof is provided for a characterization of dendrites monotonely equivalent to a universal dendrite that was originally proved using the erroneous result. Finally, in response to a question by J.J. Charatonik, it is shown that a dendrite contained in all of its monotone preimages must have a discrete set of ramification points. |
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Keywords: | Dendrite Monotone map Monotone equivalence |
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