The product of any collection of compact topological spaces, no matter how large the collection, is itself compact in the product topology. Proved by Andrey Tychonoff, it is one of the central theorems of general topology and is equivalent, in full generality, to the axiom of choice.
Facts
StatementThe product of any collection of compact topological spaces is compact in the product topology. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Sources
1. Tychonoff's Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, theorem statement sentence
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology.
lead paragraph, attribution and dating sentence
in 1935 stated the full theorem along with the remark that its proof was the same as for the special case
In Group: General Topology, Lead paragraph
In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology.
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