Springer.Srivastava.S.M.A.Course.on.Borel.Sets.(GTM.Springer,1998)

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1、AcknowledgmentsIamgratefultomanypeoplewhohavesuggestedimprovementsintheoriginalmanuscriptforthisbook.InparticularIwouldliketothankS.C.Bagchi,R.Barua,S.Gangopadhyay(n´eeBhattacharya),J.K.Ghosh,M.G.Nadkarni,andB.V.Rao.Mydeepestfeelingsofgratitudeandap-preciationarereservedforH.Sarbadhik

2、ariwhoverypatientlyreadseveralversionsofthisbookandhelpedinallpossiblewaystobringthebooktoitspresentform.ItisapleasuretorecordmyappreciationforA.MaitrawhoshowedthebeautyandpowerofBorelsetstoagenerationofIndianmathematiciansincludingme.Ialsothankhimforhissuggestionsduringtheplanningsta

3、geofthebook.IthankP.BandyopadhyaywhohelpedmeimmenselytosortoutalltheLATEXproblems.ThanksarealsoduetoR.KarforpreparingtheLATEXfilesfortheillustrationsinthebook.IamindebtedtoS.B.Rao,DirectoroftheIndianStatisticalInstituteforextendingexcellentmoralandmaterialsupport.AllmycolleaguesintheSt

4、at–MathUnitalsolentamuchneededandinvaluablemoralsupportduringthelonganddifficultperiodthatthebookwaswritten.Ithankthemall.Itakethisopportunitytoexpressmysincerefeelingsofgratitudetomychildren,RosyandRavi,fortheirgreatunderstandingofthetaskItookontomyself.Whattheymissedduringtheperiodthe

5、bookwaswrittenwillbeknowntoonlythethreeofus.Finally,Ipayhomagetomylatewife,Kiranwhoreallyunderstoodwhatmathematicsmeanttome.S.M.SrivastavaContentsAcknowledgmentsviiIntroductionxiAboutThisBookxv1CardinalandOrdinalNumbers11.1CountableSets.........................11.2OrderofInfinity......

6、..................41.3TheAxiomofChoice......................71.4MoreonEquinumerosity....................111.5ArithmeticofCardinalNumbers...............131.6Well-OrderedSets.......................151.7TransfiniteInduction......................181.8OrdinalNumbers........................2

7、11.9Alephs..............................241.10Trees...............................261.11InductiononTrees.......................291.12TheSouslinOperation.....................311.13IdempotenceoftheSouslinOperation............342TopologicalPreliminaries392.1MetricSpaces..................

8、.....