华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 8-11.

• 数学 统计学 • 上一篇    下一篇

遗传不可分解空间与具有球覆盖性质空间的关系

林丽华   

  1. 三明学院 数学与计算机科学系, 福建三明 365004
  • 收稿日期:2007-09-08 修回日期:2007-12-06 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 林丽华

Relation between hereditarily indecomposable space and spaces with the ball-covering property(Chinese)

LIN Li-hua   

  1. Department of Mathmatic and computer science, Sanming University, Sanming Fujian 365004, China
  • Received:2007-09-08 Revised:2007-12-06 Online:2008-05-25 Published:2008-05-25
  • Contact: LIN Li-hua

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摘要： 讨论Banach空间中遗传不可分解空间与具有球覆盖性质空间的关系.证明若Banach空间X具有遗传不可分解性质,且X中的Gateaux可微点在X中稠密,则空间X具有球覆盖性质;进一步得到如果X的Gateaux可微点仅在X中的某一无穷维子空间中稠密,则X仍具有球覆盖性质.

关键词: 球覆盖, Banach空间, 遗传不可分解空间, 球覆盖, Banach空间, 遗传不可分解空间

Abstract: It was shown that if X is a hereditarily indecomposable Banach space, and Gateaux differentiability points are dense in X, then X is a ball-covering property space. And further if Gateaux differentiability points are dense in a infinitely dimensional subspace of X , then X is a ball-covering property space too.

Key words: Banach space, hereditarily indecomposable space, Ball-covering, Banach space, hereditarily indecomposable space

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