拓扑空间中几类紧性非标准的研究硕士论文

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3、c:ÿÀ;üf;;5;Èf;šIO©ÛÜSïÓ‰EŒÆa¬ÆØ©TheStudyofSeveralClassesofCompactnessinTopologicalspacebyNonstandardMethodSpecialty:AppliedMathematicsName:LuLiInstructor:ChenDongliABSTRACTTopologyhaspromotedtheprogressofanalyticsgreatly.Theconceptandtech-nologyofthetopology

4、havebeenwidelyappliedtomanysubjects.Itisnecessarytostudytheproperyofcompact,whichisthekeyconceptintopology.Nonstandardanalysistheoryhasdevelopedrapidlyrecently.Ithasbeenappliedtoclassicalmathematicsandphisicstheory,especiallyinunlimitedandmicroaspect.Nonstan

5、dardanalysistheoryisintroducedtoTopologyinthispaper.Firstly,therelatedtheoryofnonstandardanalysisisdescribed,includingthestructureinnonstandardglobaldomainandstandardglobaldomain,formallanguage,andthecongurationofnonstandardmodelwithitsnature.Secondly,theto

6、pologyisredenedbymonad.Therelateddenationandcerti-cationisproposed.Finally,thenonstandardcharacterizationisprovidedincompact,locallycompact,relativelycompactsituation.Itprovesthatthenonstandardcharacterizationagreeswellwiththedenitionofnonstandardanalysi

7、s.Thenatrueofthreecompactspacepruductisobtainedbyintruducingtheconversionprincipleandinternaltheorem.Nonstandardanalysiscannotonlymakesthedenitionoriginalstandardanalysisclear,butalsosimpliesthecertication.Ithasthesameconsistencywiththenormaltopology.Also

8、,itcanimprovetheprogressthenonstandardanalysistheoryintopology.ItprovidesanovelmethodinthestudyofTomology,andhassomereferencevalueandpracticalsignicance.ÜSïÓ‰EŒÆa¬ÆØ©Keywords:topology;monad;com