連續(xù)預序集.pdf

1、南京師范大學碩士學位論文連續(xù)預序集姓名：趙娜申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：賀偉20080501AbstractInthisthesis，westudycontinuoussubsetsystemThemainresultsare：preorderedsetsandpreorderedsetsOilZ—1Inacontinuouspreorderedset，theway—belowrelationsatis腦thestrong

2、interpolationproperty(si)2Thedirectproductofafamilyofcontinuouspre。orderedsetswithminimumelement0isalsocontinuous3Theimageofacontinuouspreorderedsetunderaprojectionpreservingdirectedleastupperboundiscontinuous4Thesetofaf

3、orm價1上ItI∈LformsabasisfortheScotttopologyon8preorderedsetL5ThecategoryPOSET(CPOSET)isareflectivesubcategoryofthecategoryPRSET(CPRSET)6ThecategoryCPRSETB(objectsarecontinuouspreorderedsetsandmot—phismsareScottcontinuousfu

4、nctionswhichpreservewaybelowrelation)iscomplete7AZcontinuouspreorderedsetisaZmeetcontinuouspreorderedset。8A7_preorderedsetPisZmeetcontinuous江andonlyifforallU∈6z(P)andz∈P，wehavet(Un上z)∈az(P)。9AcontinuouspreorderedsetLisah

5、ypercontinuouspreorderedsetifandonlyiftheScotttopologyistheuppertopology。10AZpre。orderedsetPisZqu蠲icontinuousifandonlyifrz(P)ishypercontinuous。11ⅡZsubsetsystemsatisfies：A∈Z(P)，云∈‘廠辛Ui∈JA∈Z(P)，aZcontinUOuspreorderedsetisa

6、Zquasicontinuouspreorderedset12IfPisaZquasicontinuouspreorderedset，(只az(P))islocalcompact13ForaZquasicontinuouspreorderedsetP，(P；az(P)，u(尸))isapairwisecompletelyregulartopologyspace14ForaZquasicontinuouspreorderedsetP，(只