Geodesic
Lelek fan from a projective Fraïssé limit
Dana Bartošová 1   ; Aleksandra Kwiatkowska 2
1 Instituto de Matematica e Estatística Universidade de São Paulo São Paulo, Brazil
2 Department of Mathematics University of California Los Angeles, CA, U.S.A.
Fundamenta Mathematicae, Tome 231 (2015) no. 1, pp. 57-79 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm231-1-4
Mots-clés : natural quotient projective fra limit family consists finite rooted trees lelek fan using construction study properties lelek fan its homeomorphism group lelek fan projectively universal projectively ultrahomogeneous class smooth fans further homeomorphism group lelek fan totally disconnected generated every neighbourhood identity has dense conjugacy class simple

Dana Bartošová  1   ; Aleksandra Kwiatkowska  2

1 Instituto de Matematica e Estatística Universidade de São Paulo São Paulo, Brazil
2 Department of Mathematics University of California Los Angeles, CA, U.S.A. 
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Dana Bartošová; Aleksandra Kwiatkowska. Lelek fan from a projective Fraïssé limit. Fundamenta Mathematicae, Tome 231 (2015) no. 1, pp. 57-79. doi: 10.4064/fm231-1-4

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