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1、RESULTSANDPROBLEMSINCOMBINATORIALGEOMETRYV.G.Boltjanskyand1.Ts.GohbergTherightoftheUniverst/tofCambridgetoprintandselfallmannerofbooAsirasgrantedbyHenryVlllin1534TheUniversityliarprintedandpublishedtonlinuauslysince1584CAMBRIDGEUNIVERSITYPRESSCambridgeLondonNewYo
2、rkNewRochelleMelbourneSydneyPublishedbyThePressSyndicateoftheUniversityofCambridgeThePittBuilding,TrumpingtonStreet,CambridgeCB21RPp.<32East57thStreet,NewYork,NY10022,USA10StamfordRoad,Oakleigh,Melbourne3166,Australiac1-?CambridgeUniversityPress1985Firstpublished
3、1985PrintedinGreatBritainattheUniversityPress,CambridgeLibraryofCongresscataloguecardnumber:85-4187BritishLibrarycataloguinginpublicationdataBoltjansky,V.G.EResultsandproblemsincombinatorialgeometry.1.CombinatorialgeometryI.TitleII.Gohberg,IzrailIll.Teoremyizadac
4、hikombinatornoigeometric.English516:13QA167ISBN0521262984ISBN0521269237Pbk00CONTENTSForewordIntroductiontotheEnglisheditionChapter1.Partitionofasetintosetsofsmallerdiameter§1.Thediameterofaset1§2.Theproblem2§3.Asolutionoftheproblemforplanesets4(q)§4.Partitionofab
5、allIntopartsofsmallerdiameter8§5.Asolutionforthree-dimensionalbodies16§6.Borsuk'sconjectureforn-dimensionalbodies31Chapter2.ThecoveringofconvexbodieswithhomotheticbodiesandtheIlluminationproblem7t0§7.Convexsets35C00G00001(A7(AD(9)§8.Aproblemofcoveringsetswithhomo
6、theticsets38§9.Areformulationoftheproblem41§10.Solutionoftheproblemforplanesets43§11.Hadwiger'sconjecture44§12.TheIlluminationproblem46§13.Asolutionoftheilluminationproblemforplanesets49§14.Theequivalenceofthetwoproblems54§15.Someboundsforc(F)60(A7§16.Partitionan
7、dIlluminationofunboundedconvexsets632Chapter3.Somerelatedproblems§17.Borsuk'sProblemfornormedspaces69§18.TheproblemsofErd6sandKlee76§19.Someunsolvedproblems82Notes96Bibliography107.L.Therearemanyelegantresultsinthetheoryofconvexbodies'3'athatmaybefullyunderstoodb
8、yhighschoolstudents,andatthesametimebeofinteresttoexpertmathematicians.Theaimofthisbookistopresentsomeoftheseresults.Weshalldiscusscombinatorialproblemsoftheth
