7 papers
Linear orders on chainable continua
Witold Marciszewski, Julia ÅcisÅowska, Benjamin Vejnar
We define and study certain linear orders on chainable continua. Those orders depend on a sequence of chains obtained from definition of chainability and on a fixed non-principal u…
The converse to Borsuk's result on fans fails
Benjamin Vejnar
A fan is an arc-wise connected hereditarily unicoherent continuum with exactly one branching point. By a result of Borsuk, every fan is a 1-dimensional continuum that can be expres…
Dynamics on fences
Jernej ÄinÄ, Udayan B. Darji, Benjamin Vejnar
Homeomorphisms of the Cantor set play a central role in topology, dynamical systems and descriptive set theory. In parallel, several classes of fence-like spaces - such as the hair…
The Complexity of Connectedness Relations on Polish Spaces
Michal Hevessy, Yusuf Uyar, Benjamin Vejnar
We systematically investigate three different equivalence relations of connectedness: being connected by arcs, being connected by continua and being connected by chains of continua…
Chaos on Peano continua
Klára Karasová, Benjamin Vejnar
Generalizing the result of Agronsky and Ceder (1991), we prove that every Peano continuum admits a continuous transformation that is exact Devaney chaotic; that is, it has a dense…
Classification complexity of chaotic systems
Benjamin Vejnar
In this paper, we deal with the classification complexity of continuous (Devaney) chaotic systems in dimensions and using the framework of invariant descriptive set…