The Linear Space of Hausdorff Continuous Interval Functions

Authors

  • Jan Harm van der Walt Department of Mathematics and Applied Mathematics, University of Pretoria

DOI:

https://doi.org/10.11145/j.biomath.2013.11.261

Keywords:

Interval functions, vector space, vector lattice,

Abstract

In this paper we discuss the algebraic structure of the space H(X) of finite Hausdorff continuous interval functions defined on an arbitrary topological space X. In particular, we show that H(X) is a linear space over R containing C(X), the space of continuous real functions on X, as a linear subspace. In addition, we prove that the order on H(X) is compatible with the linear structure introduced here so that H(X) is an Archimedean vector lattice.

Author Biography

Jan Harm van der Walt, Department of Mathematics and Applied Mathematics, University of Pretoria

Department of Mathematics and Applied Mathematics; Senior Lecturer

Downloads

Published

2013-12-24

Issue

Section

Original Articles