论文标题
弱选择和可亚顺序的可迁移空间
Weak Selections and Suborderable Metrizable Spaces
论文作者
论文摘要
$ x $的每个连续弱选择都定义了$ x $的粗略拓扑，称为选择拓扑。拓扑由此类选择拓扑的集合确定的空间称为连续弱选择空间。对于此类空间，Garc \'ıa-Ferreira，Miyazaki，Nogura和Tomita考虑了最小数字$ \ text {cws}（x）选择拓扑的$ x $的原始拓扑，并称其为$ x $的CWS-number。在本文中，我们表明每个半订购空间$ x $的$ \ text {cws}（x）\ leq 2 $，而$ \ text {cws}（x）（x）= 2 $准确地是当这样的空间$ x $具有两个组件时，并且不可订购。互补的结果，我们还表明，对于每个可下订单的可分离空间$ x $，$ \ text {cws}（x）= 1 $，至少具有3个组件。
Each continuous weak selection for a space $X$ defines a coarser topology on $X$, called a selection topology. Spaces whose topology is determined by a collection of such selection topologies are called continuous weak selection spaces. For such spaces, Garc\'ıa-Ferreira, Miyazaki, Nogura and Tomita considered the minimal number $\text{cws}(X)$ of selection topologies which generate the original topology of $X$, and called it the cws-number of $X$. In this paper, we show that $\text{cws}(X)\leq 2$ for every semi-orderable space $X$, and that $\text{cws}(X)=2$ precisely when such a space $X$ has two components and is not orderable. Complementary to this result, we also show that $\text{cws}(X)=1$ for each suborderable metrizable space $X$ which has at least 3 components.
