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

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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 \(T_{1}\)-space, extending a result of Anguelov.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0083, Pretoria, South Africa

    Jan Harm van der Walt

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  1. Jan Harm van der Walt
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Correspondence to Jan Harm van der Walt.

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van der Walt, J.H. Vector-valued interval functions and the Dedekind completion of C(X, E). Positivity 21, 1143–1159 (2017). https://doi.org/10.1007/s11117-016-0456-7

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