A numerical scale for non locally connected planar continua
A numerical scale for non locally connected planar continua
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DOI：
10.1016/j.topol.2015.12.060
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发表时间：
2014-11
影响因子：
0.6
通讯作者：
Timo Jolivet;B. Loridant;J. Luo
中科院分区：
文献类型：
--
作者：
Timo Jolivet;B. Loridant;J. Luo
我们引入了一个数值尺度来量化平面连续体在多大程度上没有局部连接。对于局部连通的连续体，数值标度为零；对于拓扑学家的正弦曲线这样的连续体，标度为1；对于不可分解的连续体，标度是无穷的。我们利用纤维的纯拓扑框架，进一步用纤维的平凡来刻画平面连续体的局部连通性。
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.