两种预阶Fréchet-Urysohn滤波器的比较
Comparing Fréchet-Urysohn filters with two pre-orders
摘要：
$\w$上的滤子$\F$称为Fréchet-Urysohn，如果只有一个非孤立点$\w \cup \{\F\}$的空间是Fréchet-Urysohn空间，其中非孤立点的邻域由$\F$的元素确定。本文利用滤波器的两种预序来区分某些Fréchet-Urysohn滤波器：一种是Rudin-Keisler预序，另一种是Todorčević-Uzcátegui在\cite{tu05}中引入的预序.本文构造了一个大小为$\c^+$的$RK$ -链，它是每个$FU$ -滤子的$RK$ -以上.同时，我们证明了$FU$ -滤子存在无穷多个$RK$ -反链.
英文摘要：
A filter $\F$ on $\w$ is called Fréchet-Urysohn if the space with only one non-isolated point $\w \cup \{\F\}$ is a Fréchet-Urysohn space, where the neighborhoods of the non-isolated point are determined by the elements of $\F$. In this paper, we distinguish some Fréchet-Urysohn filters by using two pre-orderings of filters: One is the Rudin-Keisler pre-order and the other one was introduced by Todorčević-Uzcátegui in \cite{tu05}. In this paper, we construct an $RK$-chain of size $\c^+$ which is $RK$-above of avery $FU$-filter. Also, we show that there is an infinite $RK$-antichain of $FU$-filters.
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