论文标题
$ω$ -RUDIN空间，确定的空间和首次计数空间
$ω$-Rudin spaces, well-filtered determined spaces and first-countable spaces
论文作者
论文摘要
我们研究了一些版本的$ d $空间，过滤良好的空间和鲁丁空间，这些版本涉及各种可视性属性。主要结果包括：（i）如果$ t_0 $ space $ x $的清醒化是首先计算的，则$ x $是$ω$ -RUDIN SPACE； （ii）如果其隔离度是先进的，则每$ω$过滤的空间都会清醒； （iii）如果$ t_0 $空间是第二计数的或可以算出的，并且具有可计数的基础，则它是$ω$ -RUDIN空间； （iv）确定了每个首先计算的$ T_0 $空间； （v）在$ω$过滤的空间中，每个不可还原的封闭子集都是指向的； （vi）每个首先计数的$ω$ - 滤波器过滤$ω^\ ast $ - $ d $ -space都是清醒的。
We investigate some versions of $d$-space, well-filtered space and Rudin space concerning various countability properties. The main results include: (i) if the sobrification of a $T_0$ space $X$ is first-countable, then $X$ is an $ω$-Rudin space; (ii) every $ω$-well-filtered space is sober if its sobrification is first-countable; (iii) if a $T_0$ space is second-countable or first-countable and with a countable underlying set, then it is a $ω$-Rudin space; (iv) every first-countable $T_0$ space is well-filtered determined; (v) every irreducible closed subset in a first-countable $ω$-well-filtered space is countably-directed; (vi) every first-countable $ω$-well-filtered $ω^\ast$-$d$-space is sober.
