R-偏序集上的若干結(jié)果.pdf

1、首都師范大學(xué)碩士學(xué)位論文R偏序集上的若干結(jié)果姓名：武利剛申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：樊磊20070415AbstractTheconceptof：R—poserisproposedin【8】，thedefinitionisasfollows：suppose(』，E)isaposet∞isnaturalnumbersetwhosepartialorderisdenotedby≤；if：R=(EH)nE∞isafamilyof

2、partialordersonA，andforall17坍∈tO，加≤即，EH￡E脅flnEmEn=量，thenwecallAaposetwithpartialorderfamily咒宄posetforshortnotedwith似，￡；咒)InthepaperthroughinterestingexamplesweCallshowwhentheordersin咒approximatesomeorderthestructureofcpo

3、(completepartialorder)，algebraiccpoorcontinuouscpodocsn’thavetobepreserved，andthepresentpaperpointcsoutwhenalgebraiccpoorcontinuouscpocallbepreservedThefixedpointtheoremof：R—poserof：Rcontinuousmappingisgivenin【7】，inthepr

4、esentpaperweshowif：Reontinuousmappingis(Scott)continuousforeveryorder島，thenitisalso(Scott)continuousforE，andfurthermorethefixedpoints011thepartialorders‘d(力∈gO)frompartialorderfamilyexactlyconstructaapproximatingsequence

5、forfixedpointoffonthepartialorderwhichisapproximatedbythepartialorderfamilyBesides，wecomparethescotttopologyonpartialorderfromapproximatingpartialorderfamilyandthemisasimpleapplicationofthisresultKevwords咒poset；lattice；a