The topology of systems of hyperspaces determined by dimension functions

Details The topology of systems of hyperspaces determined by dimension functions The topology of systems of hyperspaces determined by dimension functions

2009-08-16

arxiv.org/abs/0908.2229v5

Topology, 48 (2009) 43-53

Mathematics

General Topology

12 pages

Scientific paper

Given a non-degenerate Peano continuum $X$, a dimension function $D:2^X_*\to[0,\infty]$ defined on the family $2^X_*$ of compact subsets of $X$, and a subset $\Gamma\subset[0,\infty)$, we recognize the topological structure of the system $(2^X,\D_{\le\gamma}(X))_{\alpha\in\Gamma}$, where $2^X$ is the hyperspace of non-empty compact subsets of $X$ and $D_{\le\gamma}(X)$ is the subspace of $2^X$, consisting of non-empty compact subsets $K\subset X$ with $D(K)\le\gamma$.

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