8th Croatian Mathematical Congress

Session

Topology

TOP

5 Jul 2024, 10:30

D6 (School of Applied Mathematics and Informatics, J. J. Strossmayer University of Osijek)

Conveners

Topology

• Vera Tonić (Faculty of mathematics, University of Rijeka, Croatia)

62. Hurewicz mapping theorem for asymptotic dimension of countable approximate groups

Vera Tonić (Faculty of mathematics, University of Rijeka, Croatia)

05/07/2024, 10:30

TOP: Topology

Talk

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
$\dim X\le \dim Y+\dim (f)$, 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...

105. Chaos on the Lelek fan and the Cantor fan

Goran Erceg (Faculty of Science, University of Split)

05/07/2024, 10:50

TOP: Topology

Talk

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....

162. A note on the specification property

Ivan Jelić (University of Split, Faculty of Science)

05/07/2024, 11:10

TOP: Topology

Talk

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 $(\underleftarrow{lim}(X,f),\sigma )$ has specification property. Of particular interest to us is the application of the obtained results to fans (e.g. Lelek fan).

164. Computable type of graphs

Matea Jelić (University of Split, Faculty of Civil Engineering, Architecture and Geodesy)

05/07/2024, 11:30

TOP: Topology

Talk

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...