Endpoints of smooth plane dendroids
General Topology
2024-08-27 v3
Abstract
Let be a smooth dendroid in the plane . We show that each endpoint of is arcwise accessible from , and that the space of endpoints has the property of a circle. In the event that is connected, we call a *Bellamy dendroid*. We prove that if is 1-dimensional, then contains a Bellamy dendroid or a Cantor set of arcs. In particular, if totally disconnected and 1-dimensional, then is non-Suslinian. An example is constructed to show that this is false outside the plane.
Cite
@article{arxiv.2405.01706,
title = {Endpoints of smooth plane dendroids},
author = {David S. Lipham},
journal= {arXiv preprint arXiv:2405.01706},
year = {2024}
}
Comments
12 pages, 3 figures