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Separation of ( n + 1 ) -families of sets in general position in 𝐑 n

Mircea Balaj (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper the main result in [1], concerning ( n + 1 ) -families of sets in general position in 𝐑 n , is generalized. Finally we prove the following theorem: If { A 1 , A 2 , , A n + 1 } is a family of compact convexly connected sets in general position in 𝐑 n , then for each proper subset I of { 1 , 2 , , n + 1 } the set of hyperplanes separating { A i : i I } and { A j : j I ¯ } is homeomorphic to S n + .

Six lonely runners.

Bohman, Tom, Holzman, Ron, Kleitman, Dan (2001)

The Electronic Journal of Combinatorics [electronic only]

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