On functional tightness of infinite products

A classical theorem of Malykhin says that if {Xα:α≤κ} is a family of compact spaces such that t(Xα)≤κ, for every α≤κ, then t(∏α≤κXα)≤κ, where t(X) is the tightness of a space X. In this paper we prove the following counterpart of Malykhin's theorem for functional tightness: Let {Xα:α<λ} be a family of compact spaces such that t0(Xα)≤κ for every α<λ. If λ≤2κ or λ is less than the first measurable cardinal, then t0(∏α<λXα)≤κ, where t0(X) is the functional tightness of a space X. In particular, if there are no measurable cardinals, then the functional tightness is preserved by arbitrarily large products of compacta. Our result answers a question posed by Okunev.