On the uniform density of \(C(X)\otimes C(Y)\) in \(C(X \times Y)\)
If \(X\) and \(Y\) are compact Hausdorff spaces, it is shown that every \(f \in C(X \times Y)_+\) can be approximated uniformly from below and above by elements of the form \(\sum_{i=1}^{i=n}f_ig_i\) where \(f_i\in C(X)_+\) and \(g_i\in C(Y)_+\) for \(i=1,\dots,n\). This result is then applied to the Fremlin tensor product of Archimedean Riesz spaces.
scientific article; zbMATH DE number 5643260
scientific article