Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces
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- by Alexander M. Blokh PDF
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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).References
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Additional Information
- Alexander M. Blokh
- Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294-1170
- MR Author ID: 196866
- Email: ablokh@math.uab.edu
- 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
- © Copyright 2015 American Mathematical Society
- 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
- MathSciNet review: 3359587