资源描述：
《topology without tears - sidney a. morris》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、TOPOLOGYWITHOUTTEARS1SIDNEYA.MORRISVersionofJune22,200121cCopyright1985-2001.Nopartofthisbookmaybereproducedbyanyprocesswithoutpriorwrittenpermissionfromtheauthor.2Thisbookisbeingprogressivelyupdatedandexpanded;itisanticipatedthattherewillbeaboutfifteenchaptersinall.On
2、lythosechapterswhichappearincolourhavebeenupdatedsofar.Ifyoudiscoveranyerrorsoryouhavesuggestedimprovementspleasee-mail:Sid.Morris@unisa.edu.auContentsIntroductioniii1TopologicalSpaces11.1Topology.................................21.2OpenSets............................
3、.....91.3Finite-ClosedTopology.........................131.4Postscript.................................20Appendix1:InfiniteSets21iiIntroductionTopologyisanimportantandinterestingareaofmathematics,thestudyofwhichwillnotonlyintroduceyoutonewconceptsandtheoremsbutalsoputin
4、tocontextoldoneslikecontinuousfunctions.However,tosayjustthisistounderstatethesignificanceoftopology.Itissofundamentalthatitsinfluenceisevidentinalmosteveryotherbranchofmathematics.Thismakesthestudyoftopologyrelevanttoallwhoaspiretobemathematicianswhethertheirfirstloveis(
5、orwillbe)algebra,analysis,categorytheory,chaos,continuummechanics,dynamics,geometry,industrialmathematics,mathematicalbiology,mathematicaleconomics,mathematicalfinance,mathematicalmodelling,mathematicalphysics,mathematicsofcommunication,numbertheory,numericalmathematics
6、,operationsresearchorstatistics.Topologicalnotionslikecompactness,connectednessanddensenessareasbasictomathematiciansoftodayassetsandfunctionsweretothoseoflastcentury.Topologyhasseveraldifferentbranches—generaltopology(alsoknownaspoint-settopology),algebraictopology,diff
7、erentialtopologyandtopologicalalgebra—thefirst,generaltopology,beingthedoortothestudyoftheothers.Weaiminthisbooktoprovideathoroughgroundingingeneraltopology.Anyonewhoconscientiouslystudiesaboutthefirsttenchaptersandsolvesatleasthalfoftheexerciseswillcertainlyhavesuchagro
8、unding.Forthereaderwhohasnotpreviouslystudiedanaxiomaticbranchofmathematicssuchasabstractalgebra,learningtowriteproof
