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径向集

数学中,给定线性空间上的一个集合,如果对于所有,存在,使得对任意,则称集合在点处是径向的(英語:radial)。[1]在几何上,这意味着,如果对任意,从发出朝向的线段落于中(线段长度非零但可以依赖于),则在点处是径向的。

若集合在某点是径向的,則称为該點為内点(英語:internal points)。[2][3]在此意義下,子集的所有內點的集合,稱為代数内部[1][4]

集合吸收集当且仅当其在0点处是径向的。[1]一些作者使用径向集作为吸收集的同义词,他们称一个在0点处径向的集合为径向集。[5]

参考文献

[编辑]
  1. ^ 1.0 1.1 1.2 Jaschke, Stefan; Küchler, Uwe. Coherent Risk Measures, Valuation Bounds, and ()-Portfolio Optimization. 2000. 
  2. ^ Aliprantis, C.D.; Border, K.C. Infinite Dimensional Analysis: A Hitchhiker's Guide 3. Springer. 2007: 199–200. ISBN 978-3-540-32696-0. doi:10.1007/3-540-29587-9. 
  3. ^ John Cook. Separation of Convex Sets in Linear Topological Spaces (pdf). May 21, 1988 [November 14, 2012]. (原始内容存档 (PDF)于2019-02-27). 
  4. ^ Nikolaĭ Kapitonovich Nikolʹskiĭ. Functional analysis I: linear functional analysis. Springer. 1992. ISBN 978-3-540-50584-6. 
  5. ^ Schaefer, Helmuth H. Topological vector spaces. GTM 3. New York: Springer-Verlag. 1971. ISBN 0-387-98726-6. 
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径向集
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