The interplay between algebras and lattices: Stone-Weierstrass for illustration (Q6180238)

This article is of a methodological value and illustrates the interaction between the algebraic and lattice structures of the Banach spaces of functions which by definition are uniformly closed vector subspaces of \(l_\infty(X)\) on a set \(X\). Another possibility of extending Stone-Weierstrass approximation is revealed for instance in [\textit{A.~G. Kusraev} and \textit{S.~S. Kutateladze}, ``Stone-Weierstrass approximation revisited'', Preprint, \url{arXiv:2210.14587}].