Urysohn's decomposition, and Zolotarev's theorem (Q1584148)

This paper follows Uryson's investigations on the decomposition of the \(n\)-dimensional compact into the combination of \(n+1\) zero-dimensional subsets. It is proved that in every \(n\)-dimensional metric space a countable family of zero-dimensional \(G_\delta\)-subsets exists, the combination of any \(n+1\) units of which involves the whole space. The author presents a corollary on the dimension characterization similar to Zolotarev's theorem on the intersection of topologies [\textit{V. P. Zolotarev}, Sov. Math., Dokl. 11, 1506--1509 (1971); translation from Dokl. Akad. Nauk SSSR 195, 540--543 (1970; Zbl 0217.48302)].