關(guān)于H-連通空間及Brouwer度的一些研究.pdf

1、西北大學(xué)碩士學(xué)位論文關(guān)于H連通空間及Brouwer度的一些研究姓名：馬訾偉申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：王戍堂20070401AbstractTimpaperconsistsoftwoparts，themultiplicativepropertyofHconnectedspaceandasimplifiedproofforinvariantpropertyofBromoerdegreeWhen&localhomeomorph

2、ismtobeahomeomorphismisalwaysakeyproblemintopobgyIn1935，SBanachandS，Mazurobtainedasignificant弛sw盱tothisquestionrequuedthaZthelocalhomsomorphismsbeproperWeshallfollowthis”implicit”suggestionWedevotetoH—amnectedspacefwhi擊m

3、eritsaproperlocalhome0_morphismfromanyconnected馬space鋤地Yj8hemeomorpkismthenY協(xié)called蛆Hconnectedspace)whichdefinedbyGJnngckinhisdissertationinthefirsttimewhenhestudiedthepropertiesofproperlocalhomeomorphism，Inchaptertwo，we

4、COIlsiderthemultiplicstivepropertyof日一connectedspace，andget8theoremofit，whichistheproductoftwofirstcountable死，日一connectedslDstceisalsoH—con刪whenoneofthemisparacompactorlocallycompactinthemethodsofgeneraltopologyR1r也er粥ex

5、tendtheprooftocountsbleproductcaseinductivelyTosomeextend，thisconclusiongeneralizedtheknownresult：theproductoftwofirstcountable乃，日一conne弛edspaceisalsoH—connected，whenoneofthemiscompactSoitwouldbeofmoreapplicationforH——co

6、nnectednessInchapterthree，wedisctm8theBrouwerdegreeandsimplifytheproofofitshomotopicinvariantpropertyThesimplifiedproofDe幽Onthat虢considerthegeneraldivisionratherthanbarycentricdivision011complexesKor工，whichme瞧118onlypart

7、ialsimplexesafedividedbutnoteachsimplexesHenceadividedcycleisalsoacycleSOitslinageunderachainmappingisackcletoo，Sothedegreeof妒isinvarisntThisproofindependenttheformulBdld=1whichissimplifiedandintuitionistic，andrenewedthe