Abstract
In this paper, we give a proof of a result concerning simultaneous interpolation and approximation from sublattices of the space of real continuous functions vanishing at infinity.
Highlights
Throughout this paper, we shall assume that X is a locally compact Hausdorff space
A continuous real function f on X is said to vanish at infinity if for every ε > 0 the set {x ∈ X : |f (x)| ≥ ε} is compact
A subset B of C0(X; R) is called a lattice if f ∧ g and f ∨ g belong to B whenever f ∈ B and g ∈ B
Summary
Throughout this paper, we shall assume that X is a locally compact Hausdorff space. A continuous real function f on X is said to vanish at infinity if for every ε > 0 the set {x ∈ X : |f (x)| ≥ ε} is compact. Let C0(X; R) be the vector space of all continuous real functions on X vanishing at infinity and equipped with the supremum norm. In order to show the main theorem we list some results.
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