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.

中文翻译：

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没有包含所有连续体作为唯一组件的紧凑的可计量空间

我们通过证明不存在紧致可度量化空间来回答 Piotr Minc 的问题，其组件集包含具有弧（即闭有界区间）的射线（即半开区间）的每个可度量化紧缩化的唯一拓扑副本，如剩下的。为此，我们使用来自不变描述集理论的 Borel 约简的概念。推论得出，不存在紧凑的可度量空间，使得每个连续统都同胚于该空间的一个分量。