在数学上，吉洪诺夫（Тихонов）定理断言，任意个紧致空间的乘积空间对于乘积拓扑是紧致的，这个定理1930年由吉洪诺夫(数学家) (Andrey Nikolayevich Tychonoff)(Андрей Николаевич Тихонов)发表。这个定理在微分拓扑、代数拓扑和泛函分析等领域中有诸多运用。

对有限个空间来说，这个定理没有特别之处；对无限个，无论是可数无穷还是不可数无穷，这个结论仍然成立，它依赖于乘积拓扑的定义，与选择公理（它又等价于佐恩引理）是等价的。

In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is named after Andrey Nikolayevich Tikhonov (whose surname sometimes is transcribed Tychonoff), who proved it first in 1930 for powers of the closed unit interval and in 1935 stated the full theorem along with the remark that its proof was the same as for the special case. The earliest known published proof is contained in a 1937 paper of Eduard Čech.