AI 中文总结
本文提出构造紧且非SI紧空间的新方法，引入v紧性概念并证明其相关性质，解答了Zhao、Ho及[1]提出的问题。
AI 中文摘要
本文提供了一种构造紧且非SI紧空间的新方法，从而对Zhao和Ho提出的问题给出了新解答。利用该方法，我们找到了一个可数紧但非SI紧的空间。作为推论，得到了一些新的非清醒框架，对由[1]提出的问题给出了新解答。受SI紧性定义的启发，我们引入了拓扑空间的一种新紧性概念，即v紧性，它比弱v紧性更强。我们讨论了v紧性、SI紧性和弱v紧性的若干性质，具体证明了：（1）v紧（SI紧、弱v紧）空间的所有闭子空间都是v紧（SI紧、弱v紧）的；（2）给出了上拓扑下v紧性的一个刻画；（3）给出了实数直线和Sorgenfrey直线的弱v紧子集的若干刻画。
英文摘要
In this paper, we provide a new method for constructing a compact and non SI-compact space and thus give a new answer for the question posed by Zhao and Ho. Using this method, we find a countable compact space which fails to be SI-compact. As a corollary, some new non sober frames are obtained and thus we give a new answer for a question raised by A.Jung. Inspired by the definition of SI-compactness, we introduce a new notion of compactness of topological spaces, namely, v-compactness, which is stronger than SI-compactness.Some properties of v-compactness, SI-compactness and weak v-compactness are discussed. Specifically, we prove that (1) all closed subspaces of a v-compact(SI-compact,weakly v-compact) space are v-compact (SI-compact, weakly v-compact);(2) a characterization of v-compactness for the upper topology is given; (3)some characterizations of weakly v-compact subsets of real line and Sorgenfrey line are given.
