# The topology of systems of hyperspaces determined by dimension functions - Mathematics > General Topology

Abstract: Given a non-degenerate Peano continuum $X$, a dimension function$D:2^X *\to0,\infty$ defined on the family $2^X *$ of compact subsets of $X$,and a subset $\Gamma\subset0,\infty$, we recognize the topological structureof the system $2^X,\D {\le\gamma}X {\alpha\in\Gamma}$, where $2^X$ is thehyperspace of non-empty compact subsets of $X$ and $D {\le\gamma}X$ is thesubspace of $2^X$, consisting of non-empty compact subsets $K\subset X$ with$DK\le\gamma$.

Author: T.Banakh, N.Mazurenko

Source: https://arxiv.org/