Topology: An Introduction to the Point-Set and Algebraic Areas (Dover Books on Mathematics) by Donald W. Kahn (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I am currently self-studying from this book. The proofs are (generally) well-presented, and the exercises (generally) follow from the section before. I am about halfway through and have done 95% of the exercises to this point. Some exercises seem out of place, as they lack context entirely, but they are few and far between. My biggest struggle is the notation, since it sometimes fails to match the common notation used elsewhere. Occasionally a major concept (such as equivalence of two topologies) will be mentioned in passing (one sentence) and then show up in the exercises as if you have a complete understanding of the concept. Other times a proof strategy will be suggested (“Hint: do X”) without also the justification that doing X actually provides a valid proof of the desired statement.I’m not upset to be studying from this book, but I do have to occasionally supplement it with online resources. I have definitely experienced worse math textbooks.

⭐It is the author’s ability to properly convey the ideas of the given subject that should be addressed not who the author chose to review it. Having read books by several of the “well-known’ authors in the area of Topology, i.e. Munkres, Kelley and Bourbaki, I found this book quite informative, lively and lives up to the author’s assertion that there is a definte need for books that are less dense(terse, pedantic) and which get right to the point, illustrating and presenting the material essential for an introductory exposure to Topology. The exercises are well chosen and extend the material presented in the text which is a complementary bonus since there appears an unfortunate trend in some texts to have seemingly irrelevant exercises at the end of each section. Also I found this to be good book for independent study and strongly recommend it to all highly motivated undergraduates.

⭐I find this to be an excellent treatment of concepts with have been made quite difficult in other texts.

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