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Basic Topology by Armstrong
Basic Topology by M.A. Armstrong
Used it once as textbook for a topology course. Thought it had too little point-set topology (mistake), so started the course with Introduction to Topology by Gamelin and Greene. Plan to use it again for Topology II -- Spring 2012, see also Topology 2: course.
I find Topology of Surfaces by Kinsey slightly preferable, in general. If you appreciate homology as I do, then choose the latter.
Applications are missing.
Contents
Preface.
1: Introduction.
2: Continuity.
3: Compactness and connectedness.
5: The fundamental group.
6: Triangulations.
7: Surfaces.
9: Degree and Lefschetz number.
10: Knots and covering spaces.
Appendix: Generators and relations