A numerical scale for non locally connected planar continua

@article{Jolivet2016ANS,
  title={A numerical scale for non locally connected planar continua},
  author={Timo Jolivet and Benoit Loridant and Jun Luo},
  journal={Topology and its Applications},
  year={2016},
  volume={202},
  pages={21-39}
}
  • Timo Jolivet, Benoit Loridant, Jun Luo
  • Published 2016
  • Mathematics
  • Topology and its Applications
  • 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. We use a purely topological framework of fibers and further characterize the local connectedness of a planar continuum in terms of triviality of its fibers. 

    Figures from this paper.

    Fibers and local connectedness of planar continua
    1
    A Core Decomposition of Compact Sets in the Plane
    3
    Peano Model for Planar Compacta and a Lemma by Beardon

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