Completeness of the homeomorphism relation of locally connected continua
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Abstract:
In this paper we prove that the homeomorphism relation of locally star-convex continua is a complete orbit equivalence relation. This implies that the homeomorphism relation of locally connected continua is complete. This answers a question posed by Chang and Gao [Proc. Amer. Math. Soc. 145 (2017), no. 3, 1329–1342].References
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Additional Information
- Tomasz Cieśla
- Affiliation: Faculty of Mathematics, Informatics and Mechanics, Institute of Mathematics, University of Warsaw, Banacha 2, 02-678 Warsaw, Poland
- Email: t.ciesla@mimuw.edu.pl
- Received by editor(s): October 30, 2017
- Received by editor(s) in revised form: May 2, 2018, and May 24, 2018
- Published electronically: December 3, 2018
- Additional Notes: This work was partially supported by the NCN (Polish National Science Centre) through the grant Harmonia no. 2015/18/M/ST1/00050.
- Communicated by: Heike Mildenberger
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 1269-1276
- MSC (2010): Primary 03E15, 54H05
- DOI: https://doi.org/10.1090/proc/14245
- MathSciNet review: 3896072