Hausdorff continuous interval-valued functions and quasicontinuous functions

Hausdorff continuous interval-valued functions and quasicontinuous functions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Hausdorff continuous interval-valued functions and quasicontinuous functions

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Birkhäuser / Springer Basel AG
Subject
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-010-0056-x
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Apr 9, 2010

References

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