關于有σ-點有限網的空間.pdf

1、廣西大學碩士學位論文關于有σ點有限網的空間姓名：趙俊玲申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：戴牧民1999.10.1finitedecompositionofkLet_Pb。afinitecovorofKthenPisaCFPc如vcrofKifPhasacompactfmite&compositiononetoonerefinementpiscalledacompactfinitedecompositionnetworkl7)fo

2、rXif，wheneverKcUwithKcompactandUopen證X，thenthereisafinitesubfamilyp’ofpsuctlthat艫’isaCFPCOVerofKandUp’cUDefinition3LetXbeaspace，andp2Up。：xeXsatisfies：foreachxeX，p，isanetworkofxandforeachU：V∈p，thereexistsWepsuchthatW(UnV(

3、i)驢isaweakbase15‰xifasubsetUofXisopeniffforeachY∈UthereexistsaP∈匏suchthatPcU(ii)艫isasequential—neighborhoodnetworkt5JforXifforanyP∈p。Pisasequentialneighborhoodofx(iii)pisasequentiallyopennetworkl5JfofXifforanyP∈p蔚Pisaseq

4、uentiaⅡyopensubsetofxDefinition4LetXbeaspace。asubsetYofxissaidtobeweakcompacF21證XiftheclosureofY證XiscompactinX，Definition5LetfbeamapfromasparexontoaspaceYfissaidt0boi：uductNestrongsequencecoveringweakcompactandcontinuous

5、ifthereisasnbspaceMofxsuchthatflMisastrongsequence—coveringandcontinuousmapfromA【ontoXandf_1∽nMisweakcompactinxforeachY∈YInthiswaywecandefineotherinductive，weakcompactandcontinuousmapsReaderscanreferto口1forunstateddefini

6、tionsandsymbolsTheoremlAspareXlugsau—pohRfinitec8一networkifandonlyifXisanlinageorametricspaceundel‘aninductivestrongscquencecovvfingweakcompactandcontinuousmapPmof_1斌ciencyLetfbeartinductivestrongsequencecoveringweakcomp

7、actandcontinuousmapfromsmetricspaceZontoxthenthereisasubspaceMofZsuchthatflMisastrongsequencecoverinecontinuousmapfromMontoKandf。(x)nMisweakcompactinZforeachx∈XLetg=flM，Sincezisametricspace，ithasaa—locallyfinitebase口byth

8、eclassicalNagata—Bing—SmimovmetrizationtheoremDenoted聲byU廖n：n∈N，where盧。islocallyfiniteinZforeach11∈NPutp。=Ug毋nM)：B∈聲。’p=U艫。Then艫isao—pointfmitecsnetworkforXInfactforeachx∈X，clz91(x)2clz擴‘(x)nM)iscompactin乙thenClzg_。(x)nB

9、：B∈歸。)isfinitebythelocallyfinitenessof聲。Thusaz94(x)nBnM：B∈盧。isfiniteSince∥(x)isclosedinM，c1Zg‘1(x)flM=g‘1(x)，Henceg1(x)nBnM：B∈聲。isfiniteandthereforep。ispointfiniteatpoIiIItxSo，pisopointfiniteinX1LetL=xm：m∈N)Uxobeaconverg