Lelek fan from a projective Fraïssé limit

• Autorzy: Dana Bartošová , Aleksandra Kwiatkowska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03C98: Applications of model theory
• 54F15: Continua and generalizations
• 03E15: Descriptive set theory
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 1
• Strony: 57-79

Daty

wydano

2015

Twórcy

autor

Dana Bartošová

• Instituto de Matematica e Estatística, Universidade de São Paulo, São Paulo, Brazil

autor

Aleksandra Kwiatkowska

• Department of Mathematics, University of California, Los Angeles, CA, U.S.A.

Identyfikatory

DOI

10.4064/fm231-1-4