A numerical scale for non-locally connected planar continua

作者：Jolivet, Timo; Loridant, Benoit^*; Luo, Jun

来源：Topology and Its Applications, 2016, 202: 21-39.

DOI：10.1016/j.topol.2015.12.060

• Local connectedness
• Fibers
• Numerical scale

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.

• 出版日期2016-4-1
• 单位中山大学