Paul L. Shick 
Topology 
Point-Set and Geometric

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

Table of Content

Foreword.

Acknowledgments.

1. Introduction: Intuitive Topology.

2. Background on Sets and Functions.

3. Topological Spaces.

4. More on Open and Closed Sets and Continuous Functions.

5. New Spaces from Old.

6. Connected Spaces.

7. Compact Spaces.

8. Separation Axioms.

9. Metric Spaces.

10. The Classification of Surfaces.

11. Fundamental Groups and Covering Spaces.

References.

Index.

About the author

PAUL L. SHICK, Ph D, is Professor in the Department of Mathematics and Computer Science at John Carroll University in Cleveland, Ohio. He earned a Ph D in Mathematics from Northwestern University in 1984, working in the area of stable homotopy theory. He remains active in research in algebraic topology.