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- W1986636594 abstract "Let S be a finite collection of compact convex sets in R d . Let D(S) be the largest diameter of any member of S . We say that the collection S is ?-separated if, for every 0 < k < d , any k of the sets can be separated from any other d-k of the sets by a hyperplane more than ? D(S)/2 away from all d of the sets. We prove that if S is an ? -separated collection of at least N(?) compact convex sets in R d and every 2d+2 members of S are met by a hyperplane, then there is a hyperplane meeting all the members of S . The number N(?) depends both on the dimension d and on the separation parameter ? . This is the first Helly-type theorem known for hyperplane transversals to compact convex sets of arbitrary shape in dimension greater than one." @default.
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- W1986636594 date "2001-04-01" @default.
- W1986636594 modified "2023-09-27" @default.
- W1986636594 title "A Helly-Type Theorem for Hyperplane Transversals to Well-Separated Convex Sets" @default.
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- W1986636594 doi "https://doi.org/10.1007/s00454-001-0016-0" @default.
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