This volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
This is a great little intro to topology... and one more reason to love Dover books for their tiny, inexpensive textbooks.
Well-motivated and lots of interesting problems. I can't compare it much to other topology books, but my general impression is that it covers less than Munkres.