Rational Extensions of C(X) via Hausdorff Continuous Functions

The 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.