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Accessible points of planar embeddings of tent inverse limit spaces

Volume 541 / 2019

Ana Anušić, Jernej Činč Dissertationes Mathematicae 541 (2019), 1-57 MSC: Primary 37B10, 37B45; Secondary 37E05, 54H20. DOI: 10.4064/dm776-1-2019 Published online: 1 July 2019


In this paper we study a class of embeddings of tent inverse limit spaces. We introduce techniques relying on the Milnor–Thurston kneading theory and use them to study the sets of accessible points and prime ends of given embeddings. We completely characterize the accessible points and prime ends of standard embeddings arising from the Barge–Martin construction of global attractors. In the other embeddings under study we find phenomena which do not occur in the standard embeddings. Furthermore, for the non-standard embeddings we prove that the shift homeomorphism cannot be extended to a planar homeomorphism.


  • Ana AnušićDepartamento de Matemática Aplicada
    Rua de Matão 1010 – Cidade Universitária
    05508-090 São Paulo, SP, Brazil
  • Jernej ČinčNational Supercomputing Centre IT4Innovations
    Division of the University of Ostrava
    Institute for Research and Applications of Fuzzy Modeling
    30. dubna 22
    70103 Ostrava, Czech Republic

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