Vol. 98, No. 2, 1982

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ISSN: 0030-8730
Evenly distributed subsets of Sn and a combinatorial application

Ky Fan

Vol. 98 (1982), No. 2, 323–325
Abstract

A family of nonempty subsets of the n-sphere Sn is said to be evenly distributed if every open hemisphere contains at least one set of . This paper first proves an antipodal theorem for evenly distributed families of nonempty closed subsets of Sn, and then applies it to improve a recent combinatorial result of Kneser-Lovász-Bárány.

Mathematical Subject Classification 2000
Primary: 54H25
Secondary: 05C15
Milestones
Received: 15 April 1981
Published: 1 February 1982
Authors
Ky Fan