Vietoris hyperspaces over scattered Priestley spaces

0559955 - MÚ 2023 RIV IL eng J - Journal Article
Banakh, T. - Bonnet, R. - Kubiś, Wieslaw
Vietoris hyperspaces over scattered Priestley spaces.
Israel Journal of Mathematics. Roč. 249, č. 1 (2022), s. 37-81. ISSN 0021-2172. E-ISSN 1565-8511
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : Poset-Boolean algebras
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s11856-022-2307-5

We study Vietoris hyperspaces of closed and final sets of Priestley spaces. We are particularly interested in Skula topologies. A topological space is Skula if its topology is generated by differences of open sets of another topology. A compact Skula space is scattered and moreover has a natural well-founded ordering compatible with the topology, namely, it is a Priestley space. One of our main objectives is investigating Vietoris hyperspaces of general Priestley spaces, addressing the question when their topologies are Skula and computing the associated ordinal ranks. We apply our results to scattered compact spaces based on certain almost disjoint families, in particular, Lusin families and ladder systems.
Permanent Link: https://hdl.handle.net/11104/0333078