A numerical scale for non locally connected planar continua
General Topology
2016-03-11 v1
Abstract
We introduce a numerical scale to quantify to which extent a planar continuum is not locally connected. For a locally connected continuum, the numerical scale is zero; for a continuum like the topologist's sine curve, the scale is one; for an indecomposable continuum, it is infinite. Among others, we shall pose a new problem that may be of some interest: can we estimate the scale from above for the Mandelbrot set ?
Cite
@article{arxiv.1411.6776,
title = {A numerical scale for non locally connected planar continua},
author = {Timo Jolivet and Benoît Loridant and Jun Luo},
journal= {arXiv preprint arXiv:1411.6776},
year = {2016}
}
Comments
21 pages