Noether类型的均质双曲和并矢双曲
Noetherian types of homogeneous compacta and dyadic compacta
摘要：
空间的诺特型是最小的$κ$，使得它有一个关于包容类似于$κ$的基。正如所有已知的齐次群最多具有$2^ω$的胞腔性一样，它们在诺特型和相关的基数函数方面满足相似的上界。我们证明了这些和许多其他结果这些基数函数。例如，每一个齐次并矢紧都有诺特型$ω$。假设GCH，在齐次紧$X$中的每一点都有一个局部基，该局部基在包容方面类似于$c(X)$。如果紧实中的每个点都有良拟序局部基，则某个点有可数局部$π$ -基。
英文摘要：
The Noetherian type of a space is the least $κ$ such that it has a base that is $κ$-like with respect to containment. Just as all known homogeneous compacta have cellularity at most $2^ω$, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactum has Noetherian type $ω$. Assuming GCH, every point in a homogeneous compactum $X$ has a local base that is $c(X)$-like with respect to containment. If every point in a compactum has a well-quasiordered local base, then some point has a countable local $π$-base.
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