Rational Extensions of C(X) via Hausdorff Continuous Functions

R. Anguelov

Abstract

The ring operations and the metric on C (X) are extended to the set $H_{nf}(X)$ of all nearly finite Hausdorff continuous interval valued functions and it is shown that $H_{nf}(X)$ 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.