Altomare, Francesco; Cappelletti Montano, Mirella On some density theorems in regular vector lattices of continuous functions. (English) Zbl 1127.46018 Collect. Math. 58, No. 2, 131-149 (2007). The authors consider the so-called regular locally convex vector sublattices of \(C(X,\mathbb R)\), with \(X\) a locally compact Hausdorff space. A sublattice \((E,\tau)\) is regular provided that the subspace of all compactly supported continuous functions on \(X\) is dense in \((E,\tau)\), the space \(E\) possesses a neighborhood base of the origin which consists of absolutely convex solid sublattices, and \(\tau\) is finer than the pointwise convergence topology. The authors prove some versions of the Stone-Weierstrass and Korovkin-type theorems in these regular sublattices. Reviewer: S. S. Kutateladze (Novosibirsk) Cited in 3 Documents MSC: 46E05 Lattices of continuous, differentiable or analytic functions 46E10 Topological linear spaces of continuous, differentiable or analytic functions Keywords:Stone-Weierstrass theorem; sublattice; Korovkin set PDFBibTeX XMLCite \textit{F. Altomare} and \textit{M. Cappelletti Montano}, Collect. Math. 58, No. 2, 131--149 (2007; Zbl 1127.46018) Full Text: EuDML