2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143520The ring operations and the metric on $C(X)$ are extended to the set $\mathbb{H}_{nf}(X)$ of all nearly finite Hausdorff continuous interval valued functions and it is shown that $\mathbb{H}_{nf}(X)$ is both rationally and topologically complete. Hence, the rings of quotients of $C(X)$ as well as their metric completions are represented as rings of Hausdorff continuous functions.Rings and AlgebrasClassical Analysis and ODEs54C30; 54C40; 13B02; 26E25text