Lelek fan from a projective Fraïssé limit

Dana Bartošová, and Aleksandra Kwiatkowska. "Lelek fan from a projective Fraïssé limit." Fundamenta Mathematicae 231.1 (2015): 57-79. <http://eudml.org/doc/283352>.

@article{DanaBartošová2015,
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.},
author = {Dana Bartošová, Aleksandra Kwiatkowska},
journal = {Fundamenta Mathematicae},
keywords = {Lelek fan; Fraïssé limits; homeomorphism groups},
language = {eng},
number = {1},
pages = {57-79},
title = {Lelek fan from a projective Fraïssé limit},
url = {http://eudml.org/doc/283352},
volume = {231},
year = {2015},
}

TY - JOUR
AU - Dana Bartošová
AU - Aleksandra Kwiatkowska
TI - Lelek fan from a projective Fraïssé limit
JO - Fundamenta Mathematicae
PY - 2015
VL - 231
IS - 1
SP - 57
EP - 79
AB - 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.
LA - eng
KW - Lelek fan; Fraïssé limits; homeomorphism groups
UR - http://eudml.org/doc/283352
ER -