The projective Fraïssé limit of the family of all connected finite graphs with confluent epimorphisms
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- by Włodzimierz J. Charatonik, Aleksandra Kwiatkowska and Robert P. Roe;
- Trans. Amer. Math. Soc. 378 (2025), 1081-1126
- DOI: https://doi.org/10.1090/tran/9258
- Published electronically: December 27, 2024
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Abstract:
We investigate the projective Fraïssé family of finite connected graphs with confluent epimorphisms and the continuum obtained as the topological realization of its projective Fraïssé limit. This continuum was unknown before. We prove that it is indecomposable, but not hereditarily indecomposable, one-dimensional, Kelley, pointwise self-homeomorphic, but not homogeneous. It is hereditarily unicoherent and each point is the top of the Cantor fan. Moreover, the universal solenoid, the universal pseudo-solenoid, and the pseudo-arc may be embedded in it.References
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Bibliographic Information
- Włodzimierz J. Charatonik
- Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W 12th St, Rolla, Missouri 65409-0020
- MR Author ID: 47515
- Aleksandra Kwiatkowska
- Affiliation: Institut für Mathematische Logik und Grundlagenforschung, Universität Münster, Einsteinstrasse 62, 48149 Münster, Germany; and Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
- MR Author ID: 853483
- Email: kwiatkoa@uni-muenster.de
- Robert P. Roe
- Affiliation: Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W 12th St, Rolla, Missouri 65409-0020
- MR Author ID: 149575
- Email: rroe@mst.edu
- Received by editor(s): July 8, 2023
- Received by editor(s) in revised form: March 5, 2024, May 21, 2024, and June 14, 2024
- Published electronically: December 27, 2024
- Additional Notes: The work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure and by CRC 1442 Geometry: Deformations and Rigidity.
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 1081-1126
- MSC (2020): Primary 03C98, 54D80, 54E40, 54F15, 54F50
- DOI: https://doi.org/10.1090/tran/9258