There is no compact metrizable space containing all continua as unique components (Q2042103)

In this interesting paper the author answers a question of Piotr Minc [\textit{P. Minc}, Topology Appl. 202, 47--54 (2016; Zbl 1341.54018)] 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. This result implies that there is no compact metrizable space such that every continuum is homeomorphic to exactly one component of this space. The proof is quite intricate, it employs continuum theory and Borel reductions coming from invariant descriptive set theory. This quite surprising and interesting connection between continuum theory and descriptive set theory may be useful for other problems as well.