sentences:  Studying the "strength" of Tychonoff's theorem for various restricted classes of spaces is an active area in set-theoretic topology.The analogue of Tychonoff's theorem in pointless topology does not require any form of the axiom of choice.To prove that Tychonoff's theorem in its general version implies the axiom of choice, we establish that every infinite cartesian product of non-empty sets is nonempty.