Counterexamples in Analysis (Dover Books on Mathematics)

Thesecounterexamples,arrangedaccordingtodifficultyorsophistication,dealmostlywiththepartofanalysisknownas"realvariables,"startingatthelevelofcalculus.Thefirsthalfofthebookconcernsfunctionsofarealvariable;topicsincludetherealnumbersystem,functionsandlimits,differentiation,Riemannintegration,sequences,infiniteseries,uniformconvergence,andsetsandmeasureontherealaxis.Thesecondhalf,encompassinghigherdimensions,examinesfunctionsoftwovariables,planesets,area,metricandtopologicalspaces,andfunctionspaces.Thisvolumecontainsmuchthatwillprovesuitableforstudentswhohavenotyetcompletedafirstcourseincalculus,andamplematerialofinteresttomoreadvancedstudentsofanalysisaswellasgraduatestudents.12figures.Bibliography.Index.Errata.