论文标题
像树状的连续图的微薄作曲家
Meager composants of tree-like continua
论文作者
论文摘要
如果$ m $相对于属性最大，则continuum $ x $的子集$ m $称为a \ textit {微薄的composant}。由Bellamy，Mouron和Ordoñez的问题激励，我们表明没有树状的连续体具有适当的开放式合成剂，并且每个类似树的连续体都有$ 1 $或$ 2^{\ Aleph_0} $ MEAGER Composant。我们还证明了一个分解定理：如果$ x $类似树状，并且每一个不可兼容的亚副本$ x $都不是密集的，那么$ x $的划分在微薄的成分中是上层半连续的，而微薄的作曲家的空间是一个树突。
A subset $M$ of a continuum $X$ is called a \textit{meager composant} if $M$ is maximal with respect to the property that every two of its points are contained in a nowhere dense subcontinuum of $X$. Motivated by questions of Bellamy, Mouron and Ordoñez, we show that no tree-like continuum has a proper open meager composant, and that every tree-like continuum has either $1$ or $2^{\aleph_0}$ meager composants. We also prove a decomposition theorem: If $X$ is tree-like and every indecomposable subcontinuum of $X$ is nowhere dense, then the partition of $X$ into meager composants is upper semi-continuous and the space of meager composants is a dendrite.
