论文标题
一些与波兰空间上的康托克森衍生物有关的属性
Some properties related to the Cantor-Bendixson derivative on a Polish space
论文作者
论文摘要
我们显示出任何序数为波兰空间的必要条件。我们还证明，对于每个可数的波兰空间，存在一个可数的序数数，它是上述空间的每个紧凑型可数子集的cantor-bendixson特征的第一组。此外，对于任何不可数的波兰空间，对于每个可计数的序数数和所有非零的自然数，我们都显示了该空间的紧凑型可计数子集的存在，因此其cantor-bendixson特性等于先前的数字。最后，对于每个波兰空间，我们确定了上述空间的所有紧凑型子集的分区的基数，直至同构的。
We show a necessary and sufficient condition for any ordinal number to be a Polish space. We also prove that for each countable Polish space, there exists a countable ordinal number that is an upper bound for the first component of the Cantor-Bendixson characteristic of every compact countable subset of the aforementioned space. In addition, for any uncountable Polish space, for every countable ordinal number and for all nonzero natural number, we show the existence of a compact countable subset of this space such that its Cantor-Bendixson characteristic equals the previous pair of numbers. Finally, for each Polish space, we determine the cardinality of the partition, up to homeomorphisms, of the set of all compact countable subsets of the aforesaid space.
