Ljusternik and Schnirelmann
and independently Borsuk proved the following well known result: Let H1,⋯,Hk be
closed subsets of the sphere Sn such that ⋃
i=1kHi = Sn and Hi ∩ (−Hi) = ∅ for
i = 1,⋯,k, then k ≧ n + 2.
In this paper, this result is considered from an abstract topological viewpoint: We
develope methods for the proof of generalizations of this result in the context of the
genus in the sense of A. S. Švarc.
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