2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106186We show that the operations addition and multiplication on the set $C(Ω)$ of all real continuous functions on $Ω\subseteq\mathbb{R}^n$ can be extended to the set $\mathbb{H}(Ω)$ of all Hausdorff continuous interval functions on $Ω$ in such a way that the algebraic structure of $C(Ω)$ is preserved, namely, $\mathbb{H}(Ω)$ is a commutative ring with identity. The operations on $\mathbb{H}(Ω)$ 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.General MathematicsClassical Analysis and ODEs26E99; 54C35text