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1、OPENPROBLEMSINTOPOLOGYEditedbyJanvanMillFreeUniversityAmsterdam,TheNetherlandsGeorgeM.ReedSt.EdmundHallOxfordUniversityOxford,UnitedKingdom1990NORTH-HOLLANDAMSTERDAM•NEWYORK•OXFORD•TOKYOIntroductionThisvolumegrewfromadiscussionbytheeditorsonthedifficultyoffindinggoodthesisproblemsf
2、orgraduatestudentsintopology.Althoughatanygiventimeweeachhadourownfavoriteproblems,weacknowledgedtheneedtoofferstudentsawiderselectionfromwhichtochooseatopicpeculiartotheirinterests.Oneofusremarked,“Wouldn’titbenicetohaveabookofcurrentunsolvedproblemsalwaysavailabletopulldownfrom
3、theshelf?”Theotherreplied,“Whydon’twesimplyproducesuchabook?”Twoyearslaterandnotsosimply,hereistheresultingvolume.Theintentistoprovidenotonlyasourcebookforthesis-levelproblemsbutalsoachal-lengetothebestresearchersinthefield.Ofcourse,thepresentedproblemsstillreflecttosomeextentouro
4、wnprejudices.However,aseditorswehavetriedtorepresentasbroadaperspectiveoftopologicalresearchaspossible.Thetopicsrangeoveralgebraictopology,analyticsettheory,continuatheory,digitaltopology,dimensiontheory,domaintheory,functionspaces,gener-alizedmetricspaces,geometrictopology,homo
5、geneity,infinite-dimensionaltopology,knottheory,orderedspaces,set-theoretictopology,topologicaldy-namics,andtopologicalgroups.Applicationareasincludecomputerscience,differentialsystems,functionalanalysis,andsettheory.Theauthorsareamongtheworldleadersintheirrespectiveresearchareas.
6、Akeycomponentinourspecificationforthevolumewastoprovidecurrentproblems.Problemsbecomequicklyoutdated,andanylistsoonlosesitsvalueifthestatusoftheindividualproblemsisuncertain.WehaveaddressedthisissuebyarrangingarunningupdateonsuchstatusineachvolumeofthejournalTOPOLOGYANDITSAPPLICA
7、TIONS.Thiswillbeusefulonlyifthereadertakesthetroubleofinformingoneoftheeditorsaboutsolutionsofproblemsposedinthisbook.Ofcourse,itwillalsobesufficienttoinformtheauthor(s)ofthepaperinwhichthesolvedproblemisstated.Weplanacompleterevisiontothevolumewiththeadditionofnewtopicsandauthors
8、withinfiveyears.Tokeepbookkeepingsimple,eachprob
