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Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces


Author: Alexander M. Blokh
Journal: Proc. Amer. Math. Soc. 143 (2015), 3985-4000
MSC (2010): Primary 37B45, 37E25, 54H20; Secondary 37C25, 37E05
DOI: https://doi.org/10.1090/S0002-9939-2015-12589-0
Published electronically: March 6, 2015
MathSciNet review: 3359587
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Abstract: We prove that self-mappings of uniquely arcwise connected locally arcwise connected spaces are pointwise-recurrent if and only if all their cutpoints are periodic while all endpoints are either periodic or belong to what we call ``topological weak adding machines''. We also introduce the notion of a ray complete uniquely arcwise connected locally arcwise connected space and show that for them the above ``topological weak adding machines'' coincide with classical adding machines (e.g., this holds if the entire space is compact).


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Additional Information

Alexander M. Blokh
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
Email: ablokh@math.uab.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12589-0
Keywords: Periodic points, recurrent points, pointwise-recurrent maps, uniquely arcwise connected space, locally arcwise connected space
Received by editor(s): August 25, 2013
Received by editor(s) in revised form: May 24, 2014
Published electronically: March 6, 2015
Additional Notes: The author was partially supported by NSF grant DMS–1201450
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society

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