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On some density theorems in regular vector lattices of continuous functions. (English) Zbl 1127.46018

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.

MSC:

46E05 Lattices of continuous, differentiable or analytic functions
46E10 Topological linear spaces of continuous, differentiable or analytic functions
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