View source for Template:Analogous fixed-point theorems

There are several fixed-point theorems which come in three equivalent variants: an [[algebraic topology]] variant, a combinatorial variant and a set-covering variant. Each variant can be proved separately using totally different arguments, but each variant can also be reduced to the other variants in its row. Additionally, each result in 
the top row can be deduced from the one below it in the same column.<ref>{{citation
 | last1 = Nyman | first1 = Kathryn L.
 | last2 = Su | first2 = Francis Edward | author2-link = Francis Su
 | doi = 10.4169/amer.math.monthly.120.04.346
 | issue = 4
 | journal = [[The American Mathematical Monthly]]
 | jstor = 10.4169/amer.math.monthly.120.04.346
 | mr = 3035127
 | pages = 346–354
 | title = A Borsuk–Ulam equivalent that directly implies Sperner's lemma
 | url = https://scholarship.claremont.edu/hmc_fac_pub/1150/
 | volume = 120
 | year = 2013}}</ref>

{| class="wikitable"
|-
! Algebraic topology !! Combinatorics !! Set covering 
|-
| [[Brouwer fixed-point theorem]] || [[Sperner's lemma]] || [[Knaster–Kuratowski–Mazurkiewicz lemma]]
|-
| [[Borsuk–Ulam theorem]] || [[Tucker's lemma]] || [[Lusternik–Schnirelmann theorem]]
|}
{{main other|[[Category:fixed points (mathematics)]]}}<noinclude>
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