n-Arc Connected Spaces
General Topology
2012-09-26 v1
Abstract
A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the real line, and (iv) one of a finite family of graphs. General continua that are aleph_0-ac are characterized. The complexity of characterizing n-ac graphs for n=2,3,4,5 is determined to be strictly higher than that of the stated characterization of 7-ac graphs.
Cite
@article{arxiv.1209.5451,
title = {n-Arc Connected Spaces},
author = {Benjamin Espinoza and Paul Gartside and Ana Mamatelashvili},
journal= {arXiv preprint arXiv:1209.5451},
year = {2012}
}