基于柯西理想意义下的连续$Omega$-domains
ontinuous $Omega$-domains based on Cauchy ideals
$Omega$-范畴为研究量化domain理论提供了一个很好的基本框架. 本文在假设完备剩余格$(Omega,*)$的承载格$Omega$本身还是一个连续格的条件下, 选取柯西理想描述定向完备性, 引入了 liminf 完备的 $Omega$-范畴的连续性理论. 在此基础之上, 进一步描述了 way below 关系, 代数对象以及收缩等基本概念以及它们与连续性的关系. 这些结果说明, 这种连续的 $Omega$-范畴确实可以看做量化的连续domain.
ategories enriched on a commutative, unital quantale $(Om,*)$ make a good framework of quantitative domain theory. In this paper, for a complete residuated lattice $(Omega,*)$ with $Om$ being a continuous lattice, a notion of continuity in liminf complete $Om$-categories is introduced based on the directness being described by Cauchy ideals. Moreover, the way below relations, algebraic objects and retractions are characterized and the relationships with continuity is studied. It is shown that continuous liminf complete $Om$-categories can be viewed as continuous $Omega$-domains.
赖洪亮
数学
范畴论liminf完备的$Omega$-范畴连续性柯西网柯西理想伴随way below关系
ategory theoryliminf complete $Om$-categorycontinuityauchy netauchy idealadjunctionway below relation
赖洪亮.基于柯西理想意义下的连续$Omega$-domains[EB/OL].(2014-02-01)[2025-08-03].http://www.paper.edu.cn/releasepaper/content/201402-18.点此复制
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