真理想族的上、下确界及其性质

The suprume and infium of a family of proper ideals and their properties

摘要: 研究了非空集合上真理想族的上、下确界.在非标准扩大模型中,采用单子论的研究方法,提出了非空集合上真理想族上、下确界的定义,在此基础上研究了真理想族上、下确界存在的充要条件,并得到了真理想族在上、下确界存在的条件下的一些运算性质.

Abstract: The suprume and infium of a family of proper ideals on anonempty set are studied.Meanwhile,the method of monad theory is used in the nonstandardenlarged model.And,the definition of the suprume and infium of a family ofproper ideals are introduced and some necessary and sufficient conditions oftheir existence are discussed.Furthermore,the properties of suprumeand infium of a family of proper ideals are obtained.