Compacta的一致幂与邻近对策
Uniform Powers of Compacta and the Proximal Game
摘要：
一致空间$X$的可数均匀幂（或均匀盒积）是${}^ωX$上的一种特殊拓扑，它介于吉洪诺夫拓扑和盒拓扑之间。我们解决了一个公开的问题所提出的P. Nyikos表明，如果$X$是一个紧凑的邻近空间，然后可数的均匀功率的$X$也是近端（虽然它不是紧凑的）。根据J. R. Bell和G. Gruenhage这意味着Corson紧的可数一致幂是集合正规的，可数仿紧的和Fréchet-Urysohn的。给出了关于紧空间的可数一致幂的第一可数性、实紧性的一些结果，并探讨了P. Nyikos关于半邻近空间的问题。
英文摘要：
The countable uniform power (or uniform box product) of a uniform space $X$ is a special topology on ${}^ωX$ that lies between the Tychonoff topology and the box topology. We solve an open problem posed by P. Nyikos showing that if $X$ is a compact proximal space then the countable uniform power of $X$ is also proximal (although it is not compact). By recent results of J. R. Bell and G. Gruenhage this implies that the countable uniform power of a Corson compactum is collectionwise normal, countably paracompact and Fréchet-Urysohn. We also give some results about first countability, realcompactness in countable uniform powers of compact spaces and explore questions by P. Nyikos about semi-proximal spaces.
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