Vol. 83, No. 1, 1979

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Some abstract generalizations of the Ljusternik-Schnirelmann-Borsuk covering theorem

Heinrich Steinlein

Vol. 83 (1979), No. 1, 285–296
Abstract

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.

Mathematical Subject Classification 2000
Primary: 55M30
Milestones
Received: 30 October 1978
Published: 1 July 1979
Authors
Heinrich Steinlein