sentences:  Tychonoff's theorem
  
  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.