幾乎弱θ空間和基亞緊空間.pdf

1、成都理工大學(xué)碩士學(xué)位論文幾乎弱θ空間和基亞緊空間姓名：鄧小彬申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：曹金文魏貴民20070501成都理T大學(xué)碩十學(xué)位論文Nearlyweak萬RefinableSpacesandBaseMetacompactSpacesABSTRACTInthisthesis，thecoveringandmappingmethodsareappliedtomakepreliminaryresearchofthenear

2、lyweak0refmablespace、basemetacompact、hereditarilyhyperparacompactspaces，andweobtainthefollowingresults：(1)AspaceXisnearlyweak0refinablespaceiff工isnearlydiscretelyweak0refinableexpandableandforeveryopencover鋁=U。：口∈A)ofX，t

3、henthereisadensesetDcXanda∥=U。群ofopenrefinementsofUsuchthatforeachx∈Dthereare聆∈∞and口∈Awithz∈u。andst(x，眵二)cU口≤。u，；(2)LetX=兀mx。beI∑|paracompact，thenitisweak0refinablespaceif兀。。FX。isweak0refinablespaceforeveryF∈[col‘。；(3)Fo

4、rcountableparacompaceX=n。X。，thefollowingsareequivalent：Xisweak0refinable；VF∈【co]“，兀wX。isnearlyweak0refinable；Vn∈∞，兀mX，isweak0refmablespace；(4)Letf：X辛Ybeperfectmapping，ifYisbase—metaparacompace，thenXisbase—metaparacompace

5、；(5)AspaceXisbasemetacompactifandonlyifthereisbase留ofX，麗thl歷l=∞(x)，suchthateverydirectedopencoverofXhasapoint—finiterefinementbase廚。，留c留suchthatx∈Int(st(x，留))foranyX∈x；(6)Obtainagroupofequivalentcharacterizationsofheredi