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任意的有界非空实数集都有一个最小上界。

数学中,最小上界性 (亦称上确界性,英語:least-upper bound property, LUB)[1]实数集和其他一些有序集的基础属性,与完备性等价[2] 。 集合X具有最小上界性当且仅当X的任意具有上界的非空子集均具有最小上界 (上确界),且属于X

参考文献编辑

  1. ^ Bartle and Sherbert (2011) define the "completeness property" and say that it is also called the "supremum property". (p. 39)
  2. ^ Willard says that an ordered space "X is Dedekind complete if every subset of X having an upper bound has a least upper bound." (pp. 124-5, Problem 17E.)