Shick P.L. Topology: Point-Set and Geometric

Wiley, 2007. — 280 p. — ISBN: 0470096055, 9780470096055The 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.Topology: Point–Set and Geometric features:
A short introduction in each chapter designed to motivate theideas and place them into an appropriate context
Sections with exercise sets ranging in difficulty from easy tofairly challenging
Exercises that are very creative in their approaches and workwell in a classroom setting
A supplemental Web site that contains complete and colorfulillustrations of certain objects, several learning modulesillustrating complicated topics, and animations of particularlycomplex proofs