σ-ortho緊空間的乘積和基可數(shù)仿緊空間的刻畫.pdf

1、成都理工大學(xué)碩士學(xué)位論文σtho緊空間的乘積和基可數(shù)仿緊空間的刻畫姓名：張孟英申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：曹金文魏貴民20070501壘望璺!墾蘭!TvchonoffProductsof6一orthoCompactSpaceandCharacterizationsofBaseCountablyParacompactSpaceABSTRCTThispaperismadeoftwoparts：onepartisthetycho

2、noffinfiniteproductpropertiesof口一orthocompact；Intheotherpart，weintroducethenotionofbasecountablyparacompaet，andresearchitspropertiesandequivalentcharacterizationtheoremsInthispaper，wehasgainedthefollowingresults：1、Letx=丌

3、zx，bel∑I—paracompact，xis口一orthocompact‘，nⅢLisOrorthocompactforeveryF∈【∑r2，(1)Base—countablyparacompactnessisallinverseinvariantofquasiperfectmappings(2)LetXis疋一spaceandYisnormal，f：x—Ybeabase。paraeompactmappingandco(x)≥mr

4、)IfYisbasecountablyparacompaet，thenXisbase—eountablyparacompact3、(1)LetXbebasecountablyparaeompactIfMisaclosedsubsetofXwithca(M)=m(X》。thenM、sbasecountablyparacompact(2)LetXisnormaleountablyparacompactandx=U。只，everyFisclo

5、sedandbase—countablyparaeompactrelativetoXthenXisbase。countablyparacompact4、(1)Foranormalspace，thefollowingstatementsareequivalent：①Xisbasecountablyparacompact；②thereisabase國(guó)forXwithI劈I=口(z)suchthateverycountablyopencove

6、r彩ofXhasalocallyfiniterefinementbyclosuresofmemberof歷(2)Foranormalspace，thefollowingstatementsareequivalent：①工isbasecountablyparacompact：②Xiscountablyparacompact，andthereisabase留forXwith防I=ca(x)，suchthateverybinaryopenCO

7、Verofxhasalocallvfiniterefinementbymembersof劈：(螢thereisabase歷forxwith陋『=ca(x)satisfyingthefollowingcondition：foreveryeountablyopencover彩ofX。thereisalocallyfinitecover歷’of石bymembersof歷suchthat歷irefinesKeywords：Tychonoffpr