Download Full Text (1.3 MB)

Download Preface (86 KB)

Download 1. Sets (226 KB)

Download 2. Functions (246 KB)

Download 3. Metric Spaces (267 KB)

Download 4. Applications of Metric Spaces (183 KB)

Download 5. The Greatest Lower Bound (202 KB)

Download 6. Continuous Functions in Metric Spaces (244 KB)

Download 7. Open Balls and Neighborhoods in Metric Spaces (225 KB)

Download 8. Open Sets in Metric Spaces (218 KB)

Download 9. Sequences in Metric Spaces (255 KB)

Download 10. Closed Sets in Metric Spaces (229 KB)

Download 11. Subspaces and Products of Metric Spaces (222 KB)

Download 12. Topological Spaces (258 KB)

Download 13. Closed Sets in Topological Spaces (240 KB)

Download 14. Continuity and Homeomorphisms (213 KB)

Download 15. Subspaces (186 KB)

Download 16. Quotient Spaces (324 KB)

Download 17. Compact Spaces (307 KB)

Download 18. Connected Spaces (241 KB)

Download 19. Path Connected Spaces (273 KB)

Download 20. Products of Topological Spaces (263 KB)

Download Index (104 KB)


This text is intended as a one-semester undergraduate introduction to point-set topology. It begins with concrete metric spaces and increases in abstraction to address topological spaces. It also includes applications that are not typically found in standard undergraduate topology textbooks. The book uses pre- and in-class activities to make students active participants in their learning. Through the activities and text material, students are carefully introduced to the ideas behind the definitions and theorems to help them develop intuition and understand the logic behind them.

Publication Date



Grand Valley State University Libraries


Allendale, MI

Creative Commons License

Creative Commons Attribution-Noncommercial-Share Alike 3.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.


opology, point-set topology, metric spaces, topological spaces, continuous functions

Topology: An Inquiry-Based Approach