Complexity of atriodic continua
Abstract
This dissertation investigates the relative complexity between a continuum and its proper subcontinua, in particular, providing examples of atriodic n-od-like continua. Let X be a continuum and n be an integer greater than or equal to three. If X is homeomorphic to an inverse limit of simple-n-od graphs with simplicial bonding maps and is simple-(n-1)-od-like, it is shown that the bonding maps can be simplicially factored through a simple-(n-1)-od. This implies, in particular, that X is homeomorphic to an inverse limit of simple-(n-1)-od graphs with simplicial bonding maps. This factoring is subsequently used to show that a specific inverse limit of simple-n-ods with simplicial bonding maps, having the property of every proper nondegenerate subcontinuum being an arc, is not simple-(n-1)-od-like.
Cite
@article{arxiv.0905.1978,
title = {Complexity of atriodic continua},
author = {C. T. Kennaugh},
journal= {arXiv preprint arXiv:0905.1978},
year = {2009}
}