Conveners
Topology
- Vera Tonić (Faculty of mathematics, University of Rijeka, Croatia)
In topological dimension theory, a well known Hurewicz theorem for dimension-lowering maps states that if $f:X\to Y$ is a closed map of metric spaces, then
$\dim X \leq \dim Y + \dim (f)$, where $\dim(f) := \sup\ \{ \dim(f^{-1}(y))\ | \ y\in Y\}$. This theorem was extended to asymptotic dimension $\mathrm{asdim}$, and in particular to $\mathrm{asdim}$ of groups - in 2006, Dranishnikov and...
For a given topological dynamical system $(X,f)$, where $X$ is a non-empty compact metric space and $f : X \to X $ a continuous function, we define an equivalence relation on $X$ and study quotients of dynamical systems. Using those results we produce on the Lelek fan and the Cantor fan a chaotic and mixing homeomorphism as well as a chaotic and mixing mapping, which is not a homeomorphism....
In this talk we discuss the specification property from a topological point of view. We show that dynamical system $(X,f)$, where $f$ is a surjective mapping, has specification property if and only if dynamical system $(\underset{\leftarrow}{\lim}(X,f),\sigma)$ has specification property. Of particular interest to us is the application of the obtained results to fans (e.g. Lelek fan).
In this talk we show that a topological pair of a chainable graph and the set of its endpoints has computable type.
The notion of a chainable graph is inspired by the notion of a graph - a set which consists of finitely many arcs such that distinct arcs intersect in at most one endpoint. It is known that if $G$ is a graph and $E$ set of all endpoints of $G$, that then $(G,E)$ has...
