Elementary Point-Set Topology A Transition to Advanced Mathematics

Inadditiontoservingasanintroductiontothebasicsofpoint-settopology,thistextbridgesthegapbetweentheelementarycalculussequenceandhigher-levelmathematicscourses.Theversatile,originalapproachfocusesonlearningtoreadandwriteproofsratherthancoveringadvancedtopics.BasedonlecturenotesthatweredevelopedovermanyyearsatTheUniversityofSeattle,thetreatmentisgearedtowardundergraduatemathmajorsandsuitableforavarietyofintroductorycourses.Startingwithelementaryconceptsinlogicandbasictechniquesofproofwriting,thetextdefinestopologicalandmetricspacesandsurveyscontinuityandhomeomorphism.Additionalsubjectsincludeproductspaces,connectedness,andcompactness.Thefinalchapterillustratestopology\'suseinotherbranchesofmathematicswithproofsofthefundamentaltheoremofalgebraandofPicard\'sexistencetheoremfordifferentialequations.,