Algebraic operations on the space of Hausdorff continuous interval functions

Details Algebraic operations on the space of Hausdorff continuous interval functions Algebraic operations on the space of Hausdorff continuous interval functions

2005-12-13

arxiv.org/abs/math/0512272v1

Mathematics

General Mathematics

Scientific paper

We show that the operations addition and multiplication on the set $C(\Omega)$ of all real continuous functions on $\Omega\subseteq\mathbb{R}^n$ can be extended to the set $\mathbb{H}(\Omega)$ of all Hausdorff continuous interval functions on $\Omega$ in such a way that the algebraic structure of $C(\Omega)$ is preserved, namely, $\mathbb{H}(\Omega)$ is a commutative ring with identity. The operations on $\mathbb{H}(\Omega)$ are defined in three different but equivalent ways. This allow us to look at these operations from different points of view as well as to show that they are naturally associated with the Hausdorff continuous functions.

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