1、哈爾濱工業(yè)大學碩士學位論文關于LICZPETTIS定理的研究姓名：孫李紅申請學位級別：碩士專業(yè)：基礎數學指導教師：李容錄20050601哈爾濱工業(yè)大學理學碩L學位論文AbstractThe0rliczPettisTheoremisoneofthemostinterestingandusefulresultsinfunctionalanalysisSinceafeWdecades，themathematicianspassthrought

2、heunremittingendeavor，theynotonlywillstudythescopefromtobestowonthenormspacetopromotetothelocallyconvexspace，evenisthemetricspaceMoreoverthesubseriesconvergenceexpandsunceasinglyastheinvariablescopeUntilfindingthestronge

3、stOrlicz—PettistopologyThestrongestOrlicz—PettistopologyandthelargestmappingsfamilyFwhichyieldsthistopologyinabstractdualitypairwerefirstobtainedbyprofessorLiRongluin2000Inthispaperweintroducethattheuniformlyconvergentto

4、pologyinbothconditionallyo(F，E)一sequentiallyconvergentsubsetsofFand盯(F，￡)countablycompactsubsetsofFandtheweaktopologyhavethesamesubseriesconvergentseriesforlocallyconvexspace，Finally，1gaveanespecialexampleofthetheorem，an

5、dit’SprovedwithAntosik—Mikusinskibasicmetrictheoremietheuniformlytopologybothconditionala(ca(X，x)，∑)一sequentlycompactsubsetsofca(2，爿)anda(ca(2，x)，∑)countablycompactsubsetsofca(E，x)andcr(Z，ca(Z，上))一topologyhavethesamesubs

6、eriesconvergentseriesThussomefamoustheoremsuchastheVitaliHahn—SaksandNikondymconvergenceinclassicalmeasuretheoryareimprovedKeywordsabstractdualitypair；Orlicz—PettistopologY；uniformlyconvergenttopology；subseriesconvergenc