The survey is devoted to the topological dynamics of maps defined on one-dimensional
continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or …

We establish obstructions for groups to act by homeomorphisms on dendrites. For instance,
lattices in higher rank simple Lie groups will always fix a point or a pair. The same holds for …

Accepted Manuscript Page 1 Cheng Chang, Su Gao The complexity of the classification
problem of continua Proceedings of the American Mathematical Society DOI: 10.1090/proc/13288 …

Given continua X, Y and a class F of maps between continua, define X≥ FY if there exists an
onto map f: X→ Y belonging to F. A map f: X→ Y is weakly confluent if for each …

The family of Wilder continua in the cube I n and its two subfamilies—of continuum-wise
Wilder continua and of hereditarily arcwise connected continua—are recognized as …

Abstract Given continua $ X $, $ Y $ and a class $\mathcal F $ of maps between continua,
define $ X\geq _ {\mathcal F} Y $ if there exists an onto map $ f: X\rightarrow Y $ belonging …

We introduce the notion of an invariantly universal pair $(S, E) $ where $ S $ is an analytic
quasi-order and $ E\subseteq S $ is an analytic equivalence relation. This means that for …

We prove that the homeomorphism relation between compact spaces can be continuously
reduced to the homeomorphism equivalence relation between absolute retracts, which …

THE COMPLEXITY OF CONTINUOUS EMBEDDABILITY BETWEEN DENDRITES §1.
Introduction. In [LR02] Louveau and Rosendal initiated the stu Page 1 THI; JOURNAL OF …

We are dealing with the complexity of the homeomorphism equivalence relation on some
classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We …