Topology / Wiley Series in Pure and Applied Mathematics (PDF)

The essentials of point-set topology, complete with motivation and
numerous examples

Topology: Point-Set and Geometric presents an introduction to
topology that begins with the axiomatic definition of a topology on
a set, rather than starting with metric spaces or the topology of
subsets of Rn. This approach includes many more examples, allowing
students to develop more sophisticated intuition and enabling them
to learn how to write precise proofs in a brand-new context, which
is an invaluable experience for math majors.

Along with the standard point-set topology
topics--connected and path-connected spaces, compact spaces,
separation axioms, and metric spaces--Topology covers the
construction of spaces from other spaces, including products and
quotient spaces. This innovative text culminates with topics from
geometric and algebraic topology (the Classification Theorem for
Surfaces and the fundamental group), which provide instructors with
the opportunity to choose which "capstone" best suits his or her
students.

Topology: Point-Set and Geometric features:

* A short introduction in each chapter designed to motivate the
ideas and place them into an appropriate context

* Sections with exercise sets ranging in difficulty from easy to
fairly challenging

* Exercises that are very creative in their approaches and work
well in a classroom setting

* A supplemental Web site that contains complete and colorful
illustrations of certain objects, several learning modules
illustrating complicated topics, and animations of particularly
complex proofs