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

Heinrich Steinlein

Vol. 83 (1979), No. 1, 285–296

DOI: 10.2140/pjm.1979.83.285

Abstract

Ljusternik and Schnirelmann and independently Borsuk proved the following well known result: Let H₁,⋯,H_k be closed subsets of the sphere Sⁿ such that ⋃ _i=1^kH_i = Sⁿ and H_i ∩ (−H_i) = ∅ 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