The topology of systems of hyperspaces determined by dimension functions

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 $D(K)\le\gamma$.

💡 Research Summary

The paper investigates the topological structure of families of hyperspaces that are filtered by a dimension function. Let (X) be a non‑degenerate Peano continuum and let (D:2^{X}_{*}\to