\(H(\lambda)\)-completely Hausdorff axiom on \(L\)-topological spaces. (Q1429777)

The author introduces the notion of \(H(\lambda)\)-completely Hausdorff spaces in terms of continuous functions into the refined unit \(L\)-interval \(\tilde{I}(L)\), where \(\tilde{I}(L)\) is the Hutton unit interval \(I(L)\) endowed with an \(L\)-topology which is the coarsest common refinement of the canonical \(L\)-topology on \(I(L)\) and the topological modification of the canonical \(L\)-topology. Several characterizations of these spaces are obtained. Of particular interest is the result that the refined unit \(L\)-interval \(\tilde{I}(L)\) is \(H(\lambda)\)-completely Hausdorff.