arXiv subjects

Robert P. Roe

Publications and source records attributed to Robert P. Roe.

2 recordsLinked to original sources

arXiv2024

The projective Fra\"ıssé limit of the family of all connected finite graphs with confluent epimorphisms

We investigate the projective Fra\"ıssé family of finite connected graphs with confluent epimorphisms and the continuum obtained as the topological realization of its projective Fra\"ıssé limit. This continuum was unknown before. We prove that it is indecomposable, but not hereditarily indecomposable, one-dimensional, Kelley, pointwise self-homeomorphic, but not homogeneous. It is hereditarily unicoherent and each point is the top of the Cantor fan. Moreover, the universal solenoid, the universal pseudo-solenoid, and the pseudo-arc may be embedded in it.

math.GN↗

arXiv2024

Projective Fraïssé limits of trees with confluent epimorphisms

We continue the study of projective Fraïssé limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light mappings from continuum theory as well as several properties of continua are modified so as to apply them to topological graphs. As the topological realizations of the projective Fraïssé limits we obtain the dendrite $D_3$, the Mohler-Nikiel universal dendroid, as well as new, interesting continua for which we do not yet have topological characterizations.

math.GN↗