Weakly Corson compact trees

0556313 - MÚ 2023 RIV NL eng J - Journal Article
Russo, Tommaso - Somaglia, J.
Weakly Corson compact trees.
Positivity. Roč. 26, č. 2 (2022), č. článku 33. ISSN 1385-1292. E-ISSN 1572-9281
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : coarse wedge topology * countably coarse wedge topology * tree * Valdivia compacta
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1007/s11117-022-00874-5

We introduce and study a new topology on trees, that we call the countably coarse wedge topology. Such a topology is strictly finer than the coarse wedge topology and it turns every chain complete, rooted tree into a Fréchet–Urysohn, countably compact topological space. We show the rôle of such topology in the theory of weakly Corson and weakly Valdivia compacta. In particular, we give the first example of a compact space T whose every closed subspace is weakly Valdivia, yet T is not weakly Corson. This answers a question due to Ondřej Kalenda.
Permanent Link: http://hdl.handle.net/11104/0330596