( n , m )-Fold Covers of Spheres

Abstract

A well known consequence of the Borsuk-Ulam theorem is that if the d-dimensional sphere S is covered with less than d + 2 open sets, then there is a set containing a pair of antipodal points. In this paper we provide lower and upper bounds on the minimum number of open sets, not containing a pair of antipodal points, needed to cover the d-dimensional sphere… (More)

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