开集的交性质，II。
Intersection properties of open sets, II.
摘要：
一个拓扑空间称为P_2（P_3，P_{<omega}）当且仅当它不包含两个（三个，三个以上）不可数空交开集.我们证明了（i）存在大小为2^omega的0维P_{<omega}空间，（ii）存在大小为omega_1的紧致P_{<omega}空间，（iii）大小为omega_1的紧致P_{<omega}空间的类Psi例子的存在性与ZFC无关，（iv）2 ^omega可以任意大，但每个第一可数（因此每个紧）P_2空间的基数<= omega_1，这是相容的。
英文摘要：
A topological space is called P_2 ( P_3, P_{<omega} ) if and only if it does not contain two (three, finitely many) uncountable open sets with empty intersection. We show that (i) there are 0-dimensional P_{<omega} spaces of size 2^omega, (ii) there are compact P_{<omega} spaces of size omega_1, (iii) the existence of a Psi-like examples for a compact P_{<omega} space of size omega_1 is independent of ZFC, (iv) it is consistent that 2^omega is as large as you wish but every first countable (and so every compact) P_2 space has cardinality<=omega_1.
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