Abstract
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 language | English |
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Pages (from-to) | 2147-2151 |
Number of pages | 5 |
Journal | Journal of Mathematical Sciences |
Volume | 70 |
Issue number | 6 |
DOIs | |
State | Published - Aug 1994 |