High Quality Content by WIKIPEDIA articles! In mathematics, Tychonoff's theorem states that the product of any collection of compact topological spaces is compact. The theorem is named after Andrey Nikolayevich 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 ?ech. Several texts identify Tychonoff's theorem as the single most important result in general topology; others allow it to share this honor with Urysohn's lemma.

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