Topology: Point-Set and Geometric (Repost)
Topology: Point-Set and Geometric By Paul L. Shick
2007 | 280 Pages | ISBN: 0470096055 | DJVU | 4 MB
2007 | 280 Pages | ISBN: 0470096055 | DJVU | 4 MB
The essentials of point–set topology, complete with motivation andnumerous examples Topology: Point–Set and Geometric presents an introduction totopology that begins with the axiomatic definition of a topology ona set, rather than starting with metric spaces or the topology ofsubsets of Rn. This approach includes many more examples, allowingstudents to develop more sophisticated intuition and enabling themto learn how to write precise proofs in a brand–new context, whichis an invaluable experience for math majors. Along with the standard point–set topologytopics connected and path–connected spaces, compact spaces,separation axioms, and metric spaces Topology covers theconstruction of spaces from other spaces, including products andquotient spaces. This innovative text culminates with topics fromgeometric and algebraic topology (the Classification Theorem for Surfaces and the fundamental group), which provide instructors withthe opportunity to choose which "capstone" best suits his or herstudents.