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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-4,
author = {Dana Barto\v sov\'a and Aleksandra Kwiatkowska},
title = {Lelek fan from a projective Fra\"\i ss\'e limit},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {57-79},
zbl = {06451632},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-4}
}
Dana Bartošová; Aleksandra Kwiatkowska. Lelek fan from a projective Fraïssé limit. Fundamenta Mathematicae, Tome 228 (2015) pp. 57-79. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm231-1-4/