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