中文摘要：

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≤∧（A）≤∧p且对任意x∈X有∧（A）（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.

英文摘要：

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.