Bourbaki

习题 9, § 6

标签 0B4Z,永久不变。引用为 [Bourbaki, Tag 0B4Z]。

一般拓扑, I

Bourbaki marks this one as harder than the rest.

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a) 证明有限数过滤器中更细比交的每个超滤器比其中至少一个过滤器更细(应用命题 5 of no. 4)。

b) Give an example of an ultrafilter which is finer than the intersection of an infinite family of ultrafilters, but which is not equal to any of the ultrafilters of this family (consider the family of ultrafilters on an infinite set XX each of which has a base consisting of a single point).

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Google 翻译生成的粗略草稿,质量较低。术语依照术语表,但句子可能有误;之后会由仔细的译文取代。