topology without tears

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1、TOPOLOGYWITHOUTTEARS1SIDNEYA.MORRISVersionofApril28,20102TranslationsofportionsoftheOctober2007versionofthisbookintoArabic(byMsAliaMariAlNuaimat),Chinese(byDrFushengBai),Persian(byDrAsefNazariGanjehlou),Russian(byDrEldarHajilarov),andSpanish(byDrGuillermoPineda-Villavicencio)arenowav

2、ailable.1cCopyright1985-2010.Nopartofthisbookmaybereproducedbyanyprocesswithoutpriorwrittenpermissionfromtheauthor.Ifyouwouldlikea(free)printableversionofthisbookpleasee-mailmorris.sidney@gmail.com(i)yourname,(ii)youraddress[notyouremailaddress],and(iii)stateexplicitlyyouragreementto

3、respectmycopyrightbynotprovidingthepassword,hardcopyorsoftcopyofthebooktoanyoneelse.[Teachersaremostwelcometousethismaterialintheirclassesandtelltheirstudentsaboutthisbookbutmaynotprovidetheirstudentsacopyofthebookorthepassword.Theyshouldadvisetheirstudentstoemailmeindividually.]2Thi

4、sbookisbeingprogressivelyupdatedandexpanded;itisanticipatedthattherewillbeaboutfteenchaptersinall.Ifyoudiscoveranyerrorsoryouhavesuggestedimprovementspleasee-mail:morris.sidney@gmail.comContents0Introduction50.1Acknowledgment................................70.2Readers{LocationsandPr

5、ofessions....................70.3Readers'Compliments............................80.4TheAuthor...................................151TopologicalSpaces171.1Topology....................................181.2OpenSets....................................251.3Finite-ClosedTopology............

6、................291.4Postscript....................................372TheEuclideanTopology382.1EuclideanTopology..............................392.2BasisforaTopology.............................442.3BasisforaGivenTopology.........................512.4Postscript........................

7、............583LimitPoints593.1LimitPointsandClosure...........................603.2Neighbourhoods................................653.3Connectedness.................................693.4Postscript....................................724Homeomorphisms734.1Subspaces.....................

8、............