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arXiv · 1801.01826

Compactifiable classes of compacta

A. Bartoš·J. Bobok·J. van Mill·P. Pyrih·B. Vejnar
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Abstract

We introduce the notion of compactifiable classes -- these are classes of metrizable compact spaces that can be up to homeomorphic copies ``disjointly combined'' into one metrizable compact space. This is witnessed by so-called compact composition of the class. Analogously, we consider Polishable classes and Polish compositions. The question of compactifiability or Polishability of a class is related to hyperspaces. Strongly compactifiable and strongly Polishable classes may be characterized by the existence of a corresponding family in the hyperspace of all metrizable compacta. We systematically study the introduced notions -- we give several characterizations, consider preservation under various constructions, and raise several questions.

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A. Bartoš, J. Bobok, J. van Mill, P. Pyrih, B. Vejnar. 2019-05-13. Compactifiable classes of compacta. https://doi.org/10.1016/j.topol.2019.106836

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