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Hausdorff continuous interval-valued functions and quasicontinuous functions

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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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technical University of Civil Engineering of Bucharest, 124, Lacul Tei Blvd., 036296, Bucharest, Romania

    Nicolae Dăneţ

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  1. Nicolae Dăneţ
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Correspondence to Nicolae Dăneţ.

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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

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