On the universal convergence sets

Summary In this paper we study various universal convergence sets, in connection with some problem arising from the Korovkin approximation theory. This analysis is made in the context of topological vector lattices, of commutative Banach algebras, of Banach algebras with an involution and of C ^*-algebras. Some applications and examples are given in specific function spaces and function algebras.Work performed out under the auspices of the G.N.A.F.A. (C.N.R.) and of Ministero della Pubblica Istruzione (60%) for the year 1982.