gtm180.a.course.on.borel.sets,.s.m..srivastava（borel.集教程）

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1、ACourseonBorelSetsS.M.SrivastavaSpringerAcknowledgmentsIamgratefultomanypeoplewhohavesuggestedimprovementsintheoriginalmanuscriptforthisbook.InparticularIwouldliketothankS.C.Bagchi,R.Barua,S.Gangopadhyay(n´eeBhattacharya),J.K.Ghosh,M.G.Nadkarni,andB.V.Rao.

2、Mydeepestfeelingsofgratitudeandap-preciationarereservedforH.Sarbadhikariwhoverypatientlyreadseveralversionsofthisbookandhelpedinallpossiblewaystobringthebooktoitspresentform.ItisapleasuretorecordmyappreciationforA.MaitrawhoshowedthebeautyandpowerofBorelset

3、stoagenerationofIndianmathematiciansincludingme.Ialsothankhimforhissuggestionsduringtheplanningstageofthebook.IthankP.BandyopadhyaywhohelpedmeimmenselytosortoutalltheLATEXproblems.ThanksarealsoduetoR.KarforpreparingtheLATEXfilesfortheillustrationsinthebook.

4、IamindebtedtoS.B.Rao,DirectoroftheIndianStatisticalInstituteforextendingexcellentmoralandmaterialsupport.AllmycolleaguesintheStat–MathUnitalsolentamuchneededandinvaluablemoralsupportduringthelonganddifficultperiodthatthebookwaswritten.Ithankthemall.Itakethis

5、opportunitytoexpressmysincerefeelingsofgratitudetomychildren,RosyandRavi,fortheirgreatunderstandingofthetaskItookontomyself.Whattheymissedduringtheperiodthebookwaswrittenwillbeknowntoonlythethreeofus.Finally,Ipayhomagetomylatewife,Kiranwhoreallyunderstoodw

6、hatmathematicsmeanttome.S.M.SrivastavaContentsAcknowledgmentsviiIntroductionxiAboutThisBookxv1CardinalandOrdinalNumbers11.1CountableSets.........................11.2OrderofInfinity........................41.3TheAxiomofChoice......................71.4MoreonE

7、quinumerosity....................111.5ArithmeticofCardinalNumbers...............131.6Well-OrderedSets.......................151.7TransfiniteInduction......................181.8OrdinalNumbers........................211.9Alephs..............................24

8、1.10Trees...............................261.11InductiononTrees.......................291.12TheSouslinOperation.....................311.13IdempotenceoftheSouslinOperation............342TopologicalPreliminaries