This paper deals with (composition) closed sets of operations on finite sets. For the general theory see the monograph of S. V. Yablonskij, G. P. Gavrilov and V. B. Kudryavtsev: Functions of the algebra of logic and Post classes (Russian) (1966; Zbl 0171.277). Specifically the algebra \(P_{k,2}\) of all two-valued operations on the set \(E_ k=\{0,1,...,k-1\}\) (k\(\geq 3)\) is investigated. A tool the Authors employ is the ”projection” pr from \(P_{k,2}\) to \(P_ 2:\) \(prf=g\) iff f, g are of the same arity and take the same value on arguments in \(E_ 2\). Sample of results: (i) The inverse image (under pr) of a closed set of Boolean functions containing \(0_ 1\) is finitely generated. (ii) If A is closed and contains \(0_ 1\), then \(pr^{-1}(A)\) contains a Sheffer function for \(pr^{-1}(A)\) iff A contains a Sheffer function for A. (iii) There is an infinite chain of closed sets between \(P_ k\) and \(P_{k,2}\). They also give (without proofs) the cardinalities of the sets of all closed subsets of \(P_{3,2}\) whose projection is a given \(A\subseteq P_ 2\), for various A, as well as the Hasse diagram depicting some fragments of the lattice of closed sets in \(P_{3,2}\).