最小上界性

在数学中，最小上界性 (亦称上确界性，英語：)[1] 是实数集和其他一些有序集的基础属性，与实数的完备性等价[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有最小上界 (上确界)。

任意的有界非空实数集都有一个最小上界。

参考文献
  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.)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.