拟连续相容Dcpo与超连续相容Dcpo

发布时间：2018-12-28 10:29

【摘要】：本文在拟连续Domain与超连续Domain的基础上,引入了拟连续Cdcpo与超连续Cdcpo,并且讨论了相关性质.全文内容如下：第一部分,预备知识.给出了本文将要引用的Cdcpo的基本定义,概念和结果.第二部分,首先将Cdcpo的点与点之间的waybelow关系推广到了集与集上,得到了拟连续Cdcpo,推广了Rudin引理,并得到拟连续Cdcpo与拟代数Cdcpo的等价刻画.其次定义了拟连续Cdcpo的相容拟基与相容局部拟基以及相容拟极小集,给出了拟连续Cdcpo的相容拟基与相容局部拟基的若干刻画,同时给出了保相容拟极小集的等价刻画.我们讨论了拟连续Cdcpo在某类映射下的保持性质,证明了拟连续Cdcpo在相容Scott拟连续映射与C-相容连续映射下保持不变.最后证明了拟连续Cdcpo对于Scott开集和Scott闭集都是可遗传的,以及拟连续Cdcpo的收缩还是拟连续Cdcpo.第三部分,首先定义了超连续Cdcpo,给出了它的等价刻画,并且得到了超连续Cdcpo的一些基本性质.其次证明了超连续Cdcpo的有限积仍是超连续Cdcpo,以及超连续Cdcpo的收缩仍是超连续Cdcpo并证明了超连续Cdcpo对于子Cdcpo具有遗传性.最后给出了超连续Cdcpo,交连续Cdcpo和拟连续Cdcpo三者之间的关系.
[Abstract]:On the basis of quasicontinuous Domain and supercontinuous Domain, this paper introduces quasicontinuous Cdcpo and supercontinuous Cdcpo, and discusses the related properties. The full text is as follows: the first part, preparatory knowledge. This paper gives the basic definition, concept and result of Cdcpo which will be referenced in this paper. In the second part, the waybelow relation between points of Cdcpo is generalized to set and set, and the Rudin Lemma is generalized by quasicontinuous Cdcpo, and the equivalent characterizations of quasicontinuous Cdcpo and quasi algebraic Cdcpo are obtained. Secondly, we define the compatible quasi basis and the compatible local quasibasis of quasicontinuous Cdcpo, and give some characterizations of the compatible quasi basis and the compatible local quasi basis of the quasicontinuous Cdcpo. At the same time, we give the equivalent characterizations for preserving the compatible quasi minimal sets. In this paper, we discuss the preserving properties of quasicontinuous Cdcpo under some classes of mappings, and prove that quasicontinuous Cdcpo is invariant under compatible Scott quasicontinuous mappings and C- compatible continuous mappings. Finally, it is proved that quasi continuous Cdcpo is hereditary to Scott open sets and Scott closed sets, and whether quasi continuous Cdcpo is contracted or quasi continuous Cdcpo.. In the third part, we define the equivalent characterizations of supercontinuous Cdcpo, and obtain some basic properties of supercontinuous Cdcpo. Secondly, it is proved that the finite product of supercontinuous Cdcpo is still supercontinuous Cdcpo, and the contraction of supercontinuous Cdcpo is still supercontinuous Cdcpo. It is proved that the supercontinuous Cdcpo is hereditary to the subCdcpo. Finally, the relations between supercontinuous Cdcpo, intersecting continuous Cdcpo and quasi continuous Cdcpo are given.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.1

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