序数Compactness
Ordinal Compactness
摘要：
我们引入了一个新的覆盖性质，定义在序型的序列的开放集，而不是在基数的家庭。这种紧性概念的最一般形式取决于两个序参数。在参数是基数的特殊情况下，我们得到了一个经典的概念。推广到序数，这个概念的表现方式要多样得多。我们提出了许多例子的空间满足非常相同的基数紧性的性质，但有广泛的不同的行为，相对于序紧性。与任意拓扑空间相比，对$T_1$空间得到了一个更精细的理论。序紧性的概念在小基数的空间中变得部分平凡。
英文摘要：
We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities of families. The most general form of this compactness notion depends on two ordinal parameters. In the particular case when the parameters are cardinal numbers, we get back a classical notion. Generalized to ordinal numbers, this notion turns out to behave in a much more varied way. We present many examples of spaces satisfying the very same cardinal compactness properties, but with a broad range of distinct behaviors, with respect to ordinal compactness. A much more refined theory is obtained for $T_1$ spaces, in comparison with arbitrary topological spaces. The notion of ordinal compactness becomes partly trivial for spaces of small cardinality.
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