On two topological cardinal invariants of an order-theoretic flavour
On two topological cardinal invariants of an order-theoretic flavour
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关于序论风味的两个拓扑基数不变量
DOI：
10.1016/j.apal.2012.05.011
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
S. Spadaro
中科院分区：
文献类型：
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作者：
S. Spadaro
Noether型和Noether π型是Peregudov在1997年引入的两个基数函数，它包含了俄罗斯学派早期研究的一些性质。它们的行为已经被证明是类似于细胞性，即拓扑空间中两两不相交的非空开集的大小的上确界。在这个类比的基础上，我们研究了Noether π型的κ-Suslin线，并且我们能够确定它对于每个κ直到第一个奇异基数。然后证明了关于可数支集箱积的Noether型的Chang猜想的一个推论，推广了Lajos Soukup的一个结果.我们完成PCF理论和诺特型的某些Pixley-Roy超空间之间的连接。
Noetherian type and Noetherian π-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the cellularity, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian π-type of κ-Suslin Lines, and we are able to determine it for every κ up to the first singular cardinal. We then prove a consequence of Changʼs Conjecture for ℵωregarding the Noetherian type of countably supported box products which generalizes a result of Lajos Soukup. We finish with a connection between PCF theory and the Noetherian type of certain Pixley–Roy hyperspaces.