Weakly Corson compact trees
General Topology
2022-03-16 v2 Functional Analysis
Abstract
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 Fr\'echet--Urysohn, countably compact topological space. We show the r\^{o}le of such topology in the theory of weakly Corson and weakly Valdivia compacta. In particular, we give the first example of a compact space whose every closed subspace is weakly Valdivia, yet is not weakly Corson. This answers a question due to Ond\v{r}ej Kalenda.
Cite
@article{arxiv.2106.11830,
title = {Weakly Corson compact trees},
author = {Tommaso Russo and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2106.11830},
year = {2022}
}