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arXiv · 0712.0507

Rational Extensions of C(X) via Hausdorff Continuous Functions

Roumen Anguelov
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Abstract

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.

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Roumen Anguelov. 2007-12-04. Rational Extensions of C(X) via Hausdorff Continuous Functions. https://arxiv.org/abs/0712.0507

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