论文标题
没有紧凑的Metrizable空间包含所有连续性作为独特的组件
There is no compact metrizable space containing all continua as unique components
论文作者
论文摘要
我们通过证明没有紧凑的Metrizable空间来回答PIOTR MINC的问题，其组件集包含射线的每个可分离的紧凑型的独特拓扑副本（即半开放间隔），其弧（即封闭的界限间隔）作为其余部分。为此，我们使用了来自不变的描述集理论的borel减少概念。因此，这是必然的，没有紧凑的迁移空间，因此每个连续体都是同构对此空间的一个组成部分的同构。
We answer a question of Piotr Minc by proving that there is no compact metrizable space whose set of components contains a unique topological copy of every metrizable compactification of a ray (i.e. a half-open interval) with an arc (i.e. closed bounded interval) as the remainder. To this end we use the concept of Borel reductions coming from Invariant descriptive set theory. It follows as a corollary that there is no compact metrizable space such that every continuum is homeomorphic to exactly one component of this space.
