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Lelek fan from a projective Fraïssé limit

Volume 231 / 2015

Dana Bartošová, Aleksandra Kwiatkowska Fundamenta Mathematicae 231 (2015), 57-79 MSC: 03E15, 37B05, 54F15, 03C98. DOI: 10.4064/fm231-1-4

Abstract

We show that a natural quotient of the projective Fraïssé limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of the Lelek fan and of its homeomorphism group. We show that the Lelek fan is projectively universal and projectively ultrahomogeneous in the class of smooth fans. We further show that the homeomorphism group of the Lelek fan is totally disconnected, generated by every neighbourhood of the identity, has a dense conjugacy class, and is simple.

Authors

  • Dana BartošováInstituto de Matematica e Estatística
    Universidade de São Paulo
    São Paulo, Brazil
    e-mail
  • Aleksandra KwiatkowskaDepartment of Mathematics
    University of California
    Los Angeles, CA, U.S.A.
    e-mail

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