Predavatelj: Domagoj Jelić

Abstract: We show that if $G$ is a topological graph, and $f$ is a continuous map, then the induced map $\tilde{f}$ acting on the hyperspace $C(G)$ of all connected subsets of $G$ by natural formula $\tilde{f}(C)=f(C)$ carries the same entropy as $f$. It is well known that this does not hold on the larger hyperspace of all compact subsets. Also, negative examples were given for the hyperspace $C(X)$ on some continua $X$, including dendrites.

Our work extends previous positive results obtained first for a much simpler case of compact interval by completely different tools.

This is joint work with Piotr Oprocha.