Abstract
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.
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Dedicated to Prof. W. A. J. Luxemburg on the occasion of his 80th birthday.
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Dăneţ, N. Hausdorff continuous interval-valued functions and quasicontinuous functions. Positivity 14, 655–663 (2010). https://doi.org/10.1007/s11117-010-0056-x
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DOI: https://doi.org/10.1007/s11117-010-0056-x
Keywords
- Hausdorff continuous interval-valued functions
- Quasicontinuous functions
- Lower (upper) semicontinuous functions
- Dedekind order completion