【摘要】：本文在擬連續(xù)Domain與超連續(xù)Domain的基礎(chǔ)上,引入了擬連續(xù)Cdcpo與超連續(xù)Cdcpo,并且討論了相關(guān)性質(zhì).全文內(nèi)容如下：第一部分,預(yù)備知識(shí).給出了本文將要引用的Cdcpo的基本定義,概念和結(jié)果.第二部分,首先將Cdcpo的點(diǎn)與點(diǎn)之間的waybelow關(guān)系推廣到了集與集上,得到了擬連續(xù)Cdcpo,推廣了Rudin引理,并得到擬連續(xù)Cdcpo與擬代數(shù)Cdcpo的等價(jià)刻畫(huà).其次定義了擬連續(xù)Cdcpo的相容擬基與相容局部擬基以及相容擬極小集,給出了擬連續(xù)Cdcpo的相容擬基與相容局部擬基的若干刻畫(huà),同時(shí)給出了保相容擬極小集的等價(jià)刻畫(huà).我們討論了擬連續(xù)Cdcpo在某類(lèi)映射下的保持性質(zhì),證明了擬連續(xù)Cdcpo在相容Scott擬連續(xù)映射與C-相容連續(xù)映射下保持不變.最后證明了擬連續(xù)Cdcpo對(duì)于Scott開(kāi)集和Scott閉集都是可遺傳的,以及擬連續(xù)Cdcpo的收縮還是擬連續(xù)Cdcpo.第三部分,首先定義了超連續(xù)Cdcpo,給出了它的等價(jià)刻畫(huà),并且得到了超連續(xù)Cdcpo的一些基本性質(zhì).其次證明了超連續(xù)Cdcpo的有限積仍是超連續(xù)Cdcpo,以及超連續(xù)Cdcpo的收縮仍是超連續(xù)Cdcpo并證明了超連續(xù)Cdcpo對(duì)于子Cdcpo具有遺傳性.最后給出了超連續(xù)Cdcpo,交連續(xù)Cdcpo和擬連續(xù)Cdcpo三者之間的關(guān)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.
【學(xué)位授予單位】：南京師范大學(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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