Let X be a metric continuum and n positive integer. Fn (X) the hyperspace of nonempty subsets with at most points. If 0 < m n, we consider quotient space Fnm = (X)/Fm (X). Given mapping f from into X, induced mappings fn fnm In this paper study relations among dynamics f, fn, answer some questions, by F. Barragán, A. Santiago-Santos J. Tenorio, related to properties: minimality, irreducibili...

For a Banach space $X$, we show that any family of graphs quasi-isometric to levels warped cone $\mathcal O_\Gamma Y$ is an expander with respect $X$ if and only the induced $\Gamma$-representation on $L^2(Y;X)$ has spectral gap. This provides examples are all spaces non-trivial type.

A recent result of Alon, Ben-Eliezer and Fischer establishes an induced removal lemma for ordered graphs. That is, if \(F\) is graph \(\varepsilon›0\), then there exists \(\delta_{F}(\varepsilon)›0\) such that every \(n\)-vertex \(G\) containing at most \(\delta_{F}(\varepsilon) n^{v(F)}\) copies can be made \(F\)-free by adding/deleting \(\varepsilon n^2\) edges. We prove \(\delta_{F}(\varepsi...