Publication at Faculty of Mathematics and Physics |
2021
Abstract
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. (c) 2021 Elsevier B.V. All rights reserved.