A nonparametric proof of the theorem of Lusternik and Schnirelman

Name: A nonparametric proof of the theorem of Lusternik and Schnirelman
Creator: Jost, Juergen
Keywords: Besicovitch covering lemma, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Lyusternik-Schnirelman theorem, 0101 mathematics, 01 natural sciences

Jost, Juergen

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Archiv der Mathemati...arrow_drop_down

Archiv der Mathematik

Article . 1989 . Peer-reviewed

License: Springer TDM

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Article . 1989

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https://dx.doi.org/10.1007/bf0...

Article

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A nonparametric proof of the theorem of Lusternik and Schnirelman

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1989 English Publisher:Springer Science and Business Media LLCJournal:Archiv der Mathematik, volume 53, pages 497-509 (issn: 0003-889X, eissn: 1420-8938,

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Authors: Jost, Juergen;

doi: 10.1007/bf01324725

A nonparametric proof of the theorem of Lusternik and Schnirelman

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Abstract

We provide a nonparametric proof of the Lyusternik-Schnirelman theorem. This proof avoids the technical complications of the other known proofs which arise from working with parametrized curves which amounts to lifting to a bundle with a nonfree O(2) action. Our arguments use only elementary geometric constructions and the Besicovitch covering lemma.

Related Organizations

Ruhr University Bochum
Germany

Keywords

Besicovitch covering lemma, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Lyusternik-Schnirelman theorem

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