Tranched graphs: consequences for topology and dynamics
Volume 273 / 2026
Fundamenta Mathematicae 273 (2026), 1-46
MSC: Primary 54E45; Secondary 54F15, 37B45, 54G15, 37B02
DOI: 10.4064/fm240613-5-12
Published online: 7 May 2026
Abstract
We compare quasi-graphs and generalized $\sin (1/x)$-type continua, which are two classes of continua that generalize topological graphs and contain the Warsaw circle as a nontrivial common element. We show that neither class is a subset of the other, provide some characterizations, and present illustrative examples. We unify both approaches by considering the class of tranched graphs, compare it to concepts known from the literature, and describe how the topological structure of its elements restricts possible dynamics.
