arXiv subjects

Dana Bartosova

Publications and source records attributed to Dana Bartosova.

3 recordsLinked to original sources

arXiv2015

Lelek fan from a projective Fraisse limit

We show that a natural quotient of the projective Fraisse 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.

math.GN↗

arXiv2012

More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $ω$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions with an $ω$-homogeneous ordering. We present an easy construction of such structures, expanding the jungle of extremely amenable groups.

math.DS↗

arXiv2009

Lelek's problem is not a metric problem

We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.

math.GN↗