Hausdorff拟一致性的双完备性
The bicompletion of the Hausdorff quasi-uniformity
摘要：
本文研究了$X$的非空子集构成的集合${\mathcal P}_0(X)$上的拟一致空间$(X,{\mathcal U})$的Hausdorff拟一致${\mathcal U}_H$是双完备的条件.实际上，我们提出了一个明确的方法来构造的$T_0$ -商的Hausdorff拟一致的准一致空间的双补。它被用来寻找拟一致$T_0$ -空间$(X,{\mathcal U})$的一个特征，对于这些空间，它们的双完备$(\widetilde{X},{\widetilde{\mathcal U}})$在${\mathcal P}_0(\widetilde{X})$上的Hausdorff拟一致$\widetilde{\mathcal U}_H$是双完备的。
英文摘要：
We study conditions under which the Hausdorff quasi-uniformity ${\mathcal U}_H$ of a quasi-uniform space $(X,{\mathcal U})$ on the set ${\mathcal P}_0(X)$ of the nonempty subsets of $X$ is bicomplete. Indeed we present an explicit method to construct the bicompletion of the $T_0$-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform $T_0$-spaces $(X,{\mathcal U})$ for which the Hausdorff quasi-uniformity $\widetilde{\mathcal U}_H$ of their bicompletion $(\widetilde{X},{\widetilde{\mathcal U}})$ on ${\mathcal P}_0(\widetilde{X})$ is bicomplete.
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