MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

4 \v{C}ech -&gt; &#268;ech; emended translation.

Here is Tychonoff's original proof, for powers of the unit interval. He builds a complete accumulation point of a given infinite set by transfinite recursion along the index set. On page 772 of this paper one finds the formulation of the general theorem (in my translation): "The product of compact spaces is again compact. This one One proves this theorem word for word as in he case of the compactness of the product of intervals". Some authors (Folland, see comment below and Walter Rudin in his Functional Analysis') credit \v{C}ech Čech with proving the general result but \v{C}ech's Čech's proof is the same as Tychonoff's and, based on a reading of his papers, I think Tychonoff deserves full credit for the theorem and its proof.

@Henno: not Fundamenta but Mathematische Annalen.

3 Inserted contents of comment into answer.

Here is Tychonoff's original proof, for powers of the unit interval. He builds a complete accumulation point of a given infinite set by transfinite recursion along the index set. In On page 772 of this paper he formulated one finds the formulation of the general theorem (in my translation): "The product of compact spaces is again compact. This one proves word for word as in he case of the compactness of the product of intervals". Some authors (Folland, see comment below and wrote Walter Rudin in his Functional Analysis') credit \v{C}ech with proving the general result but \v{C}ech's proof is the same as in Tychonoff's and, based on a reading of his papers, I think Tychonoff deserves full credit for the first papertheorem and its proof.

@Henno: not Fundamenta but Mathematishe Mathematische Annalen.

2 the the -> the

Here is Tychonoff's original proof, for powers of the unit interval. He builds a complete accumulation point of a given infinite set by transfinite recursion along the index set. In this paper he formulated the general theorem and wrote the the proof is the same as in the first paper. @Henno: not Fundamenta but Mathematishe Annalen.