Compactifiable classes of compacta

0507958 - MÚ 2020 RIV NL eng J - Journal Article
Bartoš, Adam - Bobok, J. - van Mill, J. - Pyrih, P. - Vejnar, B.
Compactifiable classes of compacta.
Topology and its Applications. Roč. 266, October (2019), č. článku 106836. ISSN 0166-8641. E-ISSN 1879-3207
R&D Projects: GA ČR(CZ) GA17-27844S
Institutional support: RVO:67985840
Keywords : common model * compactifiable class * complexity * homeomorphism equivalence
OECD category: Pure mathematics
Impact factor: 0.531, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.topol.2019.106836

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.
Permanent Link: http://hdl.handle.net/11104/0298925