"Weakly Corson compact trees"
Russo, TommasoWe 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 countably compact topological space. We show the role 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 Ondrej Kalenda. Joint work with Jacopo Somaglia.