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
Has Statement Form
In Branch
Principal Result Of
Source Andrey Tychonoff (Wikipedia)
Proved By
Source Tychonoff's Theorem (Wikipedia)
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
Proved By: Andrey Tychonoff, Lead sentence
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.
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.
View the Source Andrey Tychonoff (Wikipedia)
Principal Result Of: Andrey Tychonoff, Research workQuote, Principal Result Of: Andrey Tychonoff, Research work
the Tychonoff's theorem, which states that every product of arbitrarily many compact topological spaces is again compact
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