Vector-valued interval functions and the Dedekind completion of C(X,E)

Vector-valued interval functions and the Dedekind completion of C(X,E) We consider interval valued functions with values in a Banach lattice E. Certain notions of continuity introduced earlier for real interval valued functions are generalised to the more general case considered here. As an application, we characterise the Dedekind completion of the space of continuous, E-valued functions on a paracompact $$T_{1}$$ T 1 -space, extending a result of Anguelov. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Vector-valued interval functions and the Dedekind completion of C(X,E)

Positivity , Volume 21 (3) – Feb 4, 2017
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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0456-7
Publisher site
See Article on Publisher Site

Abstract

We consider interval valued functions with values in a Banach lattice E. Certain notions of continuity introduced earlier for real interval valued functions are generalised to the more general case considered here. As an application, we characterise the Dedekind completion of the space of continuous, E-valued functions on a paracompact $$T_{1}$$ T 1 -space, extending a result of Anguelov.

Journal

PositivitySpringer Journals

Published: Feb 4, 2017

References

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