Topology: An Introduction to the Point-Set and Algebraic Areas

by Donald W. Kahn

Excellent text offers comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. The text is accessible to students at the advanced undergraduate or graduate level who are conversant with the basics of real analysis or advanced calculus. Problems, with selected solutions. Bibliography. 1975 edition.

Genres: Mathematics

240 pages, Paperback

First published July 19, 1995

Reviews

[James Swenson · Rating 4 out of 5]

I learned point-set topology from this text, and later used it in a course I taught.

It's a good source, starting with a quick review of basic logic and set theory, and introducing topological ideas in a metric setting before passing to the more abstract axiomatic definition of "a" topology. Later sections cover the basic definition of manifold, the classification of surfaces, and the calculation of simple fundamental groups.

I, personally, would like to see the typography updated to something more pleasing to the eye. The few typos here should not detract from the understanding, though.

The author's afterword suggests good choices for what to read next, though the list was compiled before Algebraic Topology was published.

[Christine Cordula Dantas · Rating 4 out of 5]

I have read parts of this book and used as a reference for some ideas, specially the part on homotopy. It is a clear introduction and I recommend it. I will probably get back to it for studying other concepts.