C（X）通过Hausdorff连续函数的有理扩张
Rational Extensions of C(X) via Hausdorff Continuous Functions
摘要：
将$C(X)$上的环运算和度量推广到几乎有限Hausdorff连续区间值函数集$\mathbb{H}_{nf}(X)$上，证明了$\mathbb{H}_{nf}(X)$是有理的和拓扑完备的.因此，$C(X)$的等价环以及它们的度量完备化被表示为Hausdorff连续函数的环。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
