最小上界性

維基百科,自由的百科全書
(重新導向自最小上界公理
任意的有界非空實數集都有一個最小上界。

數學中,最小上界性 (亦稱上確界性,英語:least-upper bound property, LUB)[1]實數集和其他一些有序集的基礎屬性,與實數的完備性等價[2] 。 集合X具有最小上界性若且唯若X的任意具有上界的非空子集最小上界 (上確界)。

參考文獻[編輯]

  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.)