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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/







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