Template:Analogous fixed-point theorems
There are several fixed-point theorems which come in 3 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.[1]
| Algebraic topology | Combinatorics | Set covering |
|---|---|---|
| Brouwer fixed point theorem | Sperner's lemma | KKM lemma |
| Borsuk-Ulam theorem | Tucker's lemma | Lusternik–Schnirelmann theorem |
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