Topologies Determined by -Ideals on ω1
Topologies Determined by -Ideals on ω1
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由 ω1 上的理想确定的拓扑
DOI：
10.4153/cjm-1978-107-7
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
F. Tall
中科院分区：
文献类型：
--
作者：
S. Broverman;J. Ginsburg;K. Kunen;F. Tall
σ-理想（在子集和可数并下封闭的集合）在理论上当然是重要的-考虑第一类集，零测度集，非平稳集等。但除了观察到在某些空间中第一类σ-理想是适当的，CR-理想还没有被拓扑学家广泛研究。本文利用σ-理想的集合论性质与相关空间的拓扑性质之间的相互作用，研究了由d-理想确定的自然拓扑。
σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.