“Lusternik–Schnirelmann theorem”的意思、由来-开放百科全书

词条

Lusternik–Schnirelmann theorem

释义

Equivalent results
References

{{about|the theorem on open covers of spheres|the theorem on simple closed geodesics on spheres|theorem of the three geodesics}}

In mathematics, the Lusternik–Schnirelmann theorem, aka Lusternik–Schnirelmann–Borsuk theorem or LSB theorem, says as follows.

If the sphere Sⁿ is covered by n + 1 open sets, then one of these sets contains a pair (x, −x) of antipodal points.

It is named after Lazar Lyusternik and Lev Schnirelmann, who published it in 1930.^[1]^[2]

Equivalent results

References

1. ^{{citation | last = Bollobás | first = Béla |authorlink= Béla Bollobás | doi = 10.1017/CBO9780511816574 | isbn = 978-0-521-69395-0 | mr = 2285090 | pages = 118–119 | publisher = Cambridge University Press|location= New York | title = The art of mathematics: Coffee time in Memphis | url = https://books.google.com/books?id=ButlynVk25MC&pg=PA118 | year = 2006}}.
2. ^{{citation|first1=Lazar|last1=Lusternik|author1-link=Lazar Lyusternik|first2=Lev|last2=Schnirelmann|author2-link=Lev Schnirelmann|title=Méthodes topologiques dans les problèmes variationnels|publisher=Gosudarstvennoe Izdat.|location=Moscow|year=1930}}. {{harvtxt|Bollobás|2006}} cites pp. 26–31 of this 68-page pamphlet for the theorem.

随便看

开放百科全书收录14589846条英语、德语、日语等多语种百科知识，基本涵盖了大多数领域的百科知识，是一部内容自由、开放的电子版国际百科全书。