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Smooth fans that are endpoint rigid
- Source :
- Applied General Topology, Vol 24, Iss 2, Pp 407-422 (2023)
- Publication Year :
- 2023
- Publisher :
- Universitat Politècnica de València, 2023.
-
Abstract
- Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.
Details
- Language :
- English
- ISSN :
- 15769402, 19894147, and 08551898
- Volume :
- 24
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Applied General Topology
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.085518989eb245ffab30e07e1aa3edaf
- Document Type :
- article
- Full Text :
- https://doi.org/10.4995/agt.2023.17922