000			01810 a2200277 4500
999			_c53397 _d53397
008			200917b ||||| |||| 00| 0 eng d
020			_a9780486453170
082			_a514.72 _bWAL
100			_aWallace, Andrew
245			_aDifferential topology: first steps
260			_bDover Publications, _c1996. _aMineola:
300			_axiii, 130 p.: ill.; _bpb; _c22 cm.
365			_aUSD _b9.95
440			_aDover books on mathematics
504			_aIncludes bibliographical references (p. 127-128) and index.
520			_aKeeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of differential topology, the theory of critical points of functions on a differentiable manifold. Additional topics include an investigation of level manifolds corresponding to a given function and the concept of spherical modifications. The text concludes with applications of previously discussed material to the classification problem of surfaces and guidance, along with suggestions for further reading and study.
650			_aMathematics
650			_aTopology
650			_aTopological space
650			_aDifferentiable Manifolds
650			_aSubmanifolds
650			_aTangent sapce
650			_acritical points
650			_aSpherical modification
942			_2ddc _cTD