Vector-valued interval functions and the Dedekind completion of \(C(X,E)\)
type: Item
instance of: scholarly article
title: Vector-valued interval functions and the Dedekind completion of \(C(X,E)\)
zbMATH Open document ID: 1386.46038
author: Jan Harm Van Der Walt
published in: Positivity
publication date: 2017-12-06T00:00:00Z
review text: The author extends the result of the paper [\textit{R. Anguelov}, Quaest. Math. 27, No. 2, 153--169 (2004; Zbl 1062.54017)] by giving the description of the Dedekind completion of the space \(C(X,E)\) with \(X\) a paracompact space and \(E\) a Banach lattice with order-continuous norm.
Mathematics Subject Classification ID: 46E40
Mathematics Subject Classification ID: 46E05
Mathematics Subject Classification ID: 46A40
zbMATH DE Number: 6816289
zbMATH Keywords: Banach-lattice-valued functions
zbMATH Keywords: Dedekind completion
zbMATH Keywords: interval analysis
reviewed by: S. S. Kutateladze
MaRDI profile type: Publication
full work available at URL: s11117-016-0456-7
OpenAlex ID: W2584781605
cites work: Dedekind Order Completion ofC(X) by Hausdorff Continuous Functions
cites work: The convergence space of minimal USCO mappings
cites work: Q3922085
cites work: Solving large classes of nonlinear systems of PDEs
cites work: Order convergence structure onC(X)
cites work: DOMINATED EXTENSIONS OF CONTINUOUS AFFINE FUNCTIONS WITH RANGE AN ORDERED BANACH SPACE
cites work: Piecewise linear approximations of set-valued maps
cites work: Extensions of Lipschitz selections and an application to differential inclusions
cites work: A calculus for set-valued maps and set-valued evolution equations
cites work: Q4652051
cites work: Q4256552
cites work: Optimization and nonsmooth analysis
cites work: The Normal Completion of the Lattice of Continuous Functions
cites work: When is every Hausdorff continuous interval-valued function bounded by continuous functions?
cites work: Banach lattices of continuous Banach lattice-valued functions
cites work: Q3688668
cites work: The normal completion of a subset of a complete lattice and lattices of continuous functions
cites work: The Second Dual of the Space of Continuous Functions. IV
cites work: Q4214669
cites work: Q5638775
cites work: Biomathematics and Interval Analysis: A Prosperous Marriage
cites work: Banach lattices
cites work: Continuous selections. I
cites work: Q5566070
cites work: Q3207999
cites work: Convex Analysis
cites work: Q3999282
cites work: The Riesz Space of Minimal Usco Maps
cites work: The Linear Space of Hausdorff Continuous Interval Functions
cites work: Linear and quasi-linear spaces of set-valued maps
DOI: 10.1007/S11117-016-0456-7
description: scientific article; zbMATH DE number 6816289