Arcs in the Plane
General Topology
2009-06-16 v1 Logic
Abstract
Assuming PFA, every uncountable subset E of the plane meets some C^1 arc in an uncountable set. This is not provable from MA(aleph_1), although in the case that E is analytic, this is a ZFC result. The result is false in ZFC for C^2 arcs, and the counter-example is a perfect set.
Cite
@article{arxiv.0906.2753,
title = {Arcs in the Plane},
author = {Joan E. Hart and Kenneth Kunen},
journal= {arXiv preprint arXiv:0906.2753},
year = {2009}
}
Comments
14 pages