全聚点集与(?)_α-紧性

豪斯道夫曾以邻域O_ε(x)中含有集A的至少一点,无限多点,不可数多点来定义集A的接触点,极限点和凝聚点。 用同样的方法,邦德列雅金在《连续群》一书中又提出完全凝聚点的概念,即我们本文中的全聚点。 在这篇文章中,我们引进了全聚点和-紧性的概念,讨论了全聚点集的并、交运算,及它们的基本性质,简单地介绍了全密集、全闭集和全聚集的概念。     

全聚点集与(?)α-紧性

In this paper we introduce the concept for the set of complete cluster point and (?)_α-cormpactness in the metric space. We have proved several primitive properties relatedto the complete cluster point and set of complete cluster point. We have discussed the relationship among some kinds of (?)_α-compactness; and analysed the relationship among the (?)_α-compactness and the general compactness. We have found that the (?)_α-compactness and the general compactness are eqivalent to each other in the metric space.