Weakly Corson compact trees

Banach spaces of continuous functions without norming Markushevich bases

“…Importantly, this assumption assures that every two elements 𝑠, 𝑡 ∈ 𝑇 admit an infimum 𝑠 ∧ 𝑡; indeed, 𝑠 ∧ 𝑡 = max( ŝ ∩ t). We refer the reader to [24,28,29,32,34,35] for more information on the coarse wedge topology and relation between this topology and classes of non-metrizable compacta. Let us only point out that by [ Combining the above lemma with Proposition 4.1, we immediately arrive at the following corollary.…”

“…Importantly, this assumption assures that every two elements $$s,t\in T$$ admit an infimum $$s\wedge t$$; indeed, $$s\wedge t=\max (\hat{s}\cap \hat{t})$$. We refer the reader to [24, 28, 29, 32, 34, 35] for more information on the coarse wedge topology and relation between this topology and classes of non‐metrizable compacta. Let us only point out that by [29, Theorem 2.8] a tree is Corson if and only if every chain is countable, in particular if $$\operatorname{ht}(T)\leqslant \omega _1$$, then T is a Corson compact space.…”