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[1]中定理3.6是经典的Dini定理的推广。Wolk在证明了这个定理后指出,有例子说明,若将值域空间Y的全无序集(即反链)有限性条件去掉后,此定理将不成立。于是他提出了一个可供进一步思考的问题:是否可用另外一些拓扑代替Y中的Dedekind拓扑,去掉Y中全无序集有限性条件后,此定理或它的某种变形依然成立?按照这个思路我们将[1]中定理3.6和3.9进行了推广。为此,先摘录两个主要概念如下: 相似文献
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It is shown that for any directed quasi ordered set (Q,≤),there is a minimal ordinal number λ such that every cofinal subset of Q contains a cofinal subset which is the o-th class original set of a λ-th class chain of Q. A special case of our results gives necessary and sufficient conditions for a directed set to contain a cofinal chain. 相似文献
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