| Abstract: | For a linear sublattice  of C(X), the set of all real continuous functions on the completely regular space X, we denote by A() the smallest uniformly closed and inverse-closed subalgebra of C(X) that contains . In this paper we study different methods to generate A() from . For that, we introduce some families of functions which are defined in terms of suprema or sums of certain countably many functions in . And we prove that A() is the uniform closure of each of these families. We obtain, in particular, a generalization of a known result about the generation of A() when is a uniformly closed linear sublattice of bounded functions. |
