Highlyregardedforitsexceptionalclarity,imaginativeandinstructiveexercises,andfinewritingstyle,thisconcisebookoffersanidealintroductiontothefundamentalsoftopology.Originallyconceivedasatextforaone-semestercourse,itisdirectedtoundergraduatestudentswhosestudiesofcalculussequencehaveincludeddefinitionsandproofsoftheorems.Thebook’sprincipalaimistoprovideasimple,thoroughsurveyofelementarytopicsinthestudyofcollectionsofobjects,orsets,thatpossessamathematicalstructure.TheauthorbeginswithaninformaldiscussionofsettheoryinChapter1,reservingcoverageofcountabilityforChapter5,whereitappearsinthecontextofcompactness.InthesecondchapterProfessorMendelsondiscussesmetricspaces,payingparticularattentiontovariousdistancefunctionswhichmaybedefinedonEuclideann-spaceandwhichleadtotheordinarytopology.Chapter3takesuptheconceptoftopologicalspace,presentingitasageneralizationoftheconceptofametricspace.Chapters4and5aredevotedtoadiscussionofthetwomostimportanttopologicalproperties:connectednessandcompactness.Throughoutthetext,Dr.Mendelson,aformerProfessorofMathematicsatSmithCollege,hasincludedmanychallengingandstimulatingexercisestohelpstudentsdevelopasolidgraspofthematerialpresented.
