摘要
本文研究了连续d-cone的Sandwich性质,证明连续d-cone的Sandwich性质关于乘积和连续线性收缩封闭.特别地,本文证明了:设X是连续domain,C是连续d-cone,下述两条等价:(1)任给Scott连续映射^q,^p:X×C→-R+满足^q≤^p,若对任意x∈X,^q(x,-),^p(x,-):C→-R+分别是超线性的和子线性的,则存在Scott连续函数∧^:X×C→-R+使得^q≤^Λ≤^p且对任意x∈X有^Λ(x,-):C→-R+是线性函数;(2)X是离散domain即X的任意两个不同元素不可比较.该结果回答了2009年Tix,Keimel和Plotkin提出的一个公开问题.
In this paper, we investigate the Sandwich property of continuous d-cones and show that the Sandwich property of continuous d-cones is closed under products and continuous retractions. Particularly, it is proved that for a continuous domain X and a continuous d-cone C, the following conditions are e- quivalent ： （1） for two continuous maps q,p：X × C → R＋with q ≤p, for any x ∈X,q（x,-）,p（x,-）： C→R＋ are superlinear and sublinear respectively, then there exists a continuous function A ：X × C→ R＋ such that q ≤∧ ≤p and∧（x,-）.-C→ R＋ is linear for all∈ E X. （2） X is a discrete domain. This result answers an open question by Tix, Keimel and Plotkin in 2009.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第5期863-867,共5页
Journal of Sichuan University(Natural Science Edition)
基金
国家自然科学基金(11371262)
关键词
Sandwich性质
线性函数
Continuous d-cone
Sandwich property
Linear function
