格拓撲的范疇性質(zhì)和若干緊性研究.pdf

1、浙江師范大學碩士學位論文格拓撲的范疇性質(zhì)和若干緊性研究姓名：陶波申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：周武能20040501RESERCHESoNTHECATEGoRYPRoPERTIESoFLATTICEToPoLoGYANDSoMECoMPACTNESSESABSTRACTInthefirstsectionofthispaper，anewkindofparacompactnessbasedontheconceptofrelati

2、veremoteneighborhoodfamilyinL—topologicalspacesisestablishedTherelationshipsbetweenthisparacompactnessandtheotherparaconlpactncssesarediscussedManypropertiessuchasL—goodextension，hereditarywithrespecttoclosedsubsets，weak

3、lytopologicalpropertyandstrenthening五seperatedpropernesaregottenAndinthissection，thesub—baseleInInaiIl$一ultIa—paracompactnessisprovedandthesubbaselemmasoftheotherparaeompactnessesarealsoprovedbyrneansofthemethodusedin一ul

4、tra“paracOmpactspacesInthesecondsection，anotherapplicationofrelativeremoteneighborhoodfaInilyisIeseaIchedThenearlyultra—fuzzyconlpactnessisgeneralizationofuItra—fuzzycorllpactIlessin工一topologicalspacesTherelationshipsbet

5、WeenthjscompactnessandtheothercompactnessarediscussedItpossessesmanythepropertiessuchashereditarywithrespecttegularclosedsubsets，weaklyt()poligicalproperty】thesubbaselemmaandtheproducttheoremAtthesametirne，thecharacCeriz

6、aCionsofthenearlyultra—fUzzycompactnessbyfiltersand11etsaIeintr()dllcedInthethiIdsection，theconceptofSL—closurespaceisintroducedbyan—otherLF—set，i，esemi—closedsetItisageneralizationofS—closureoperatorinL—topologicalspace