本文選題：連續(xù)格 + 半連續(xù)格　； 參考：《淮北師范大學(xué)》2015年碩士論文

【摘要】：自從19世紀(jì)七十年代連續(xù)格與代數(shù)格被發(fā)現(xiàn)以后,連續(xù)格理論便成為了極為活躍的研究領(lǐng)域,對(duì)連續(xù)格理論的拓展也逐漸加深.半素理想是Y.Ray最先提出的并得到了進(jìn)一步豐富；伍秀華等通過(guò)利用半素理想,定義出來(lái)另外的一種新型關(guān)系,并運(yùn)用到半連續(xù)格當(dāng)中；同樣可以進(jìn)行等價(jià)刻畫(huà)的還有半連續(xù)dcpo或相容連續(xù)Domain的性質(zhì),而在本文第三章節(jié)把這些思想延伸到愈發(fā)寬泛的相關(guān)理論的拓展當(dāng)中.自從D.S.Scott首次提出了Domain的概念,國(guó)內(nèi)外數(shù)學(xué)家對(duì)Domain理論便產(chǎn)生極大的興趣并進(jìn)行深入研究,得到了連續(xù)Domain的許多類(lèi)似于連續(xù)格的性質(zhì).第四、五章從廣義的角度,從連續(xù)格的內(nèi)蘊(yùn)特征出發(fā)引入了偽相容連續(xù)Domain、偽相容連續(xù)Domain局部基的相關(guān)概念及性質(zhì).本文主要包括六個(gè)部分：第一章：緒論知識(shí).主要介紹了本論文的研究現(xiàn)狀、研究背景、研究意義,并扼要概述了本文所要研究的主要內(nèi)容.第二章：預(yù)備知識(shí).將全文將要用到的連續(xù)Domain理論相關(guān)的概念與結(jié)果等預(yù)備知識(shí)作了簡(jiǎn)要概述.第三章：本章研究半連續(xù)dcpo的局部半基的若干理論.主要研究連續(xù)格,半連續(xù)格.半連續(xù)dcpo強(qiáng)連續(xù)dcpo等的相關(guān)定義與主要性質(zhì)的內(nèi)部聯(lián)系以及拓展方法,通過(guò)弱化與強(qiáng)化,比較拓展,得到它們的聯(lián)系與區(qū)別,并做出一些補(bǔ)充.而對(duì)于連續(xù)偏序集,相容連續(xù)偏序集,弱Domain, exact Domain等的一些結(jié)論也類(lèi)似可得.最后給出半連續(xù)dcpo的局部半基的概念,從而得到一些相關(guān)性質(zhì)與結(jié)論.第四章：本章研究偽相容連續(xù)Domain本章根據(jù)相容Domain,引出了偽相容連續(xù)Domain與它的基的概念.進(jìn)一步得出若干等價(jià)命題及相關(guān)性質(zhì)的證明,從而將得出許多良好的性質(zhì)與結(jié)論,從而對(duì)Domain理論作出進(jìn)一步推廣.而在本章最后介紹了在偽相容連續(xù)偏序集中一類(lèi)特殊的相容定向集.第五章：本章研究偽相容連續(xù)Domain局部基的若干性質(zhì).本章在上一章的基礎(chǔ)上引入相容定向集的容元,容集,以及偽相容連續(xù)Domain的局部基的概念,在此基礎(chǔ)上討論了偽相容連續(xù)Domain中容元的局部基的特點(diǎn),并對(duì)偽相容連續(xù)Domain的局部基的其它重要相關(guān)性質(zhì)進(jìn)一步探討.第六章：作為格理論中的一類(lèi)比較特殊的元素,交既約元具有一些很好的性質(zhì),在格論中也占有重要的地位.本章通過(guò)引入連續(xù)交既約元的概念,對(duì)交既約元的性質(zhì)展開(kāi)探討.
[Abstract]:Since the discovery of continuous lattices and algebraic lattices in the 1870s, the theory of continuous lattices has become a very active research field, and the extension of the theory of continuous lattices has gradually deepened. The semi-prime ideal was first put forward by Y.Ray and further enriched, Wu Xiuhua and others defined another new relationship by using semi-prime ideal, and applied it to semicontinuous lattice. There are also the properties of semicontinuous dcpo or compatible continuous Domain which can also be characterized as equivalent. In the third chapter of this paper we extend these ideas to the extension of more and more extensive related theories. Since D.S.Scott first put forward the concept of Domain, mathematicians at home and abroad have had great interest in the theory of Domain and studied it in depth. Many properties of continuous Domain similar to continuous lattices have been obtained. In the fourth and fifth chapters, the concepts and properties of pseudo-compatible continuous Domain local bases are introduced from the generalized point of view and from the intrinsic characteristics of continuous lattices. This article mainly includes six parts: chapter one: introduction knowledge. This paper mainly introduces the research status, research background, research significance, and briefly summarizes the main contents of this paper. Chapter two: preparatory knowledge. The concepts and results of continuous Domain theory which will be used in this paper are briefly summarized. Chapter 3: in this chapter, we study some theories of local semilobars of semicontinuous dcpo. We mainly study continuous lattice and semi-continuous lattice. The relative definitions of semicontinuous dcpo strongly continuous dcpo and the internal relations of its main properties, as well as its extension methods, are obtained by weakening and strengthening, comparing and expanding, and some additions are made. For continuous partial ordered sets, consistent continuous partial ordered sets, weak Domain, exact Domain and so on, some results are similar. Finally, the concept of local semi-basis of semicontinuous dcpo is given, and some related properties and conclusions are obtained. Chapter 4: this chapter studies pseudo-compatible continuous Domain. According to compatible domain, we introduce the concept of pseudo-compatible continuous Domain and its basis. Some equivalent propositions and related properties are further proved, and many good properties and conclusions will be obtained, thus further generalizing the Domain theory. At the end of this chapter, we introduce a class of special compatible orientations in pseudo-compatible continuous partial ordering sets. Chapter 5: in this chapter, we study some properties of pseudo-compatible continuous Domain local basis. On the basis of the previous chapter, this chapter introduces the concepts of the local basis of the compatible direction-set, the capacitive set, and the pseudo-compatible continuous Domain. On this basis, the characteristics of the local basis of the component in the pseudo-compatible continuous Domain are discussed. The other important properties of the local basis of pseudo-compatible continuous Domain are further discussed. Chapter 6: as a kind of special element in lattice theory, the intersection irreducible element has some good properties and plays an important role in lattice theory. By introducing the concept of continuous intersection irreducible elements, this chapter discusses the properties of intersection irreducible elements.
【學(xué)位授予單位】：淮北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類(lèi)號(hào)】：O153.1

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