Tikhonov's theorem or Tychonoff's theorem can refer to any of several mathematical theorems named after the Russian mathematician Andrey Nikolayevich Tikhonov:
- Tychonoff's theorem, which states that the product of any collection of compact topological spaces is compact
- Tikhonov's fixed point theorem, concerning fixed points of continuous mappings on compact subsets of certain topological vector spaces
- Tikhonov's theorem (dynamical systems), concerning limiting behaviour of solutions of systems of differential equations applicable to (among other things) chemistry
- Tychonoff's uniqueness theorem, concerning the one-dimensional heat equation
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