The Jung inequality for transfinite diameters

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The following analog of Jung's theorem on coverings of a compact disk is proved. For each continuum E ⊂ C, there exists a unique covering E of the disk with minimal radius R(E), and here R(E) ≤ 2d(E), where d(E) is the transfinite diameter of E; we have R(e)=2d(E) only in the case of a line segment. Applications of this result are given.

Original languageEnglish
Pages (from-to)2147-2151
Number of pages5
JournalJournal of Mathematical Sciences
Issue number6
StatePublished - Aug 1994


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