sentences:  This criterion leads to a proof (Kelley, 1950) of Tychonoff's theorem, which is, word for word, identical to the Cartan/Bourbaki proof using filters, save for the repeated substitution of "universal net" for "ultrafilter base".5) A proof using nets but not universal nets was given in 1992 by Paul Chernoff.All of the above proofs use the axiom of choice (AC) in some way.