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Borsuk–Ulam theorem
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== References == * {{cite journal| first=Karol| last=Borsuk|title=Drei Sätze über die ''n''-dimensionale euklidische Sphäre| journal=[[Fundamenta Mathematicae]]| volume=20|year=1933|pages=177–190| author-link=Karol Borsuk| url=http://matwbn.icm.edu.pl/ksiazki/fm/fm20/fm20117.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://matwbn.icm.edu.pl/ksiazki/fm/fm20/fm20117.pdf |archive-date=2022-10-09 |url-status=live| language=de| doi=10.4064/fm-20-1-177-190| doi-access=free}} * {{cite journal|first1=Lazar|last1=Lyusternik|author-link1=Lazar Lyusternik|first2=Lev|last2=Shnirel'man|author-link2=Lev Schnirelmann|title=Topological Methods in Variational Problems|journal=Issledowatelskii Institut Matematiki I Mechaniki Pri O. M. G. U.|location=Moscow|year=1930}} * {{cite book| author-link=Jiří Matoušek (mathematician)| first=Jiří |last=Matoušek| title=Using the Borsuk–Ulam theorem|title-link=Using the Borsuk–Ulam Theorem|publisher=Springer Verlag|location=Berlin|year=2003|isbn=978-3-540-00362-5|doi=10.1007/978-3-540-76649-0}} * {{cite journal|first=H.|last=Steinlein|title=Borsuk's antipodal theorem and its generalizations and applications: a survey. Méthodes topologiques en analyse non linéaire|journal=Sém. Math. Supér. Montréal, Sém. Sci. OTAN (NATO Adv. Study Inst.) |volume= 95|year=1985|pages=166–235}} * {{cite journal | title = Borsuk-Ulam Implies Brouwer: A Direct Construction | first = Francis Edward | last = Su | journal = The American Mathematical Monthly | volume = 104 | number = 9 | date = Nov 1997 | pages = 855–859 | url = http://www.math.hmc.edu/~su/papers.dir/borsuk.pdf | doi = 10.2307/2975293 | jstor = 2975293 | citeseerx = 10.1.1.142.4935 | access-date = 2006-04-21 | archive-url = https://web.archive.org/web/20081013051302/http://www.math.hmc.edu/~su/papers.dir/borsuk.pdf | archive-date = 2008-10-13 | url-status = dead }}
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