In the paper it is shown that every Hausdorff continuous interval-valued function corresponds uniquely to an equivalence class of quasicontinuous functions. This one-to-one correspondence is used to construct the Dedekind order completion of C(X), the set of all real-valued continuous functions, when X is a compact Hausdorff topological space or a complete metric space.
Positivity – Springer Journals
Published: Apr 9, 2010
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