Small Valdivia compacta and trees
Claudia Correa, Daniel V. Tausk

TL;DR
This paper characterizes small Valdivia compact spaces using tree path spaces and constructs a counterexample to a conjecture on twisted sums of $C(K)$ spaces under $ riangle$.
Contribution
It provides a new characterization of small Valdivia compacta via trees and constructs a counterexample to a related conjecture under $ riangle$.
Findings
Characterization of small Valdivia compacta through tree path spaces
Counterexample to a conjecture on twisted sums of $C(K)$ spaces under $ riangle$
Advances understanding of the structure of Valdivia compacta
Abstract
We present a characterization of Valdivia compact spaces of small weight in terms of path spaces of trees and we use it to obtain (under ) a counterexample to a conjecture related to an open problem concerning twisted sums of spaces.
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