Tychonoff's theorem
Product of any collection of compact topological spaces is compact / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Tychonoff's theorem?
Summarize this article for a 10 year old
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 1935 article by Tychonoff, "Über einen Funktionenraum".[1]
Tychonoff's theorem is often considered as perhaps the single most important result in general topology (along with Urysohn's lemma).[2] The theorem is also valid for topological spaces based on fuzzy sets.[3]