膨胀柯西滤子：构造一般一致空间完备化的一种方法
一般拓扑
2013-10-22 v3
摘要
强调一致性与一致空间概念的《一般拓扑学》论著，在定义完备一致空间的概念以及通过柯西序列构造度量空间的完备化方面，当然不会遇到困难。相比之下，构造一般一致空间的完备化，尤其是不借助伪度量时，显得有些棘手。本注记提出了“膨胀柯西滤子”的概念作为实现这一目标的方法。作者后来得知，所有内容实际上已在 Bourbaki 的《一般拓扑学》1966 年版中阐述（其中滤子被称为“极小柯西滤子”而非“膨胀柯西滤子”），因此本注记已被作者撤回。
引用
@article{arxiv.1309.1748,
title = {Inflated Cauchy Filters - A Way to Construct the Completion of a General Uniform Space},
author = {Eliahu Levy},
journal= {arXiv preprint arXiv:1309.1748},
year = {2013}
}
备注
A note of 4 pages. v2: some corrections of typos and language improvements. This paper has been withdrawn by the author because, contrary to the impression I had had, Bourbaki, in their 1966 edition, expound essentially the same thing. This was kindly brought to my attention later by Prof. Hans-Peter Kunzi of the University of Cape Town