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best book for topology?
Introductory book on Topology

I have been charged with ordering some topology books for our library. The books must be intended for undergraduates. I have thought of:

Topology: by Munkres

Topology from a Differentiable Viewpoint: by Milnor

Algebraic Topology: by Hatcher

A Combinatorial Introduction to Topology: by Henle

Homology Theory: by Vick

Topology: by Hocking and Young

From Calculus to Cohomology: by Madsen and Tornehave

Are there some good books that I am missing?

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Maybe not: it looks like Joe is searching more on the realm of Algebraic Topology, not just General Topology. –  a.r. Sep 13 '12 at 18:50
    
@AgustíRoig Good point. Perhaps OP would like to look at What algebraic topology book to read after Hatcher's? –  MJD Sep 13 '12 at 18:51
    
Or Learning Roadmap for Algebraic Topology, or one of the other articles that comes up if you do a search for articles tagged "algebraic-topology" and "reference-request". –  MJD Sep 13 '12 at 18:52
    
@MJD. Thanks. I realize that almost everything has already been answered here. :-D –  a.r. Sep 13 '12 at 18:54
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marked as duplicate by Mikko Korhonen, MJD, William, rschwieb, Michael Greinecker Sep 13 '12 at 20:41

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

4 Answers

up vote 4 down vote accepted

I might also recommend checking out the following (reviews are generally well accepted and they are Dover (except the last) books, so the price is excellent):

Introduction to Topology: Third Edition (Dover Books on Mathematics) Bert Mendelson (Author), Mathematics (Author)

Counterexamples in Topology (Dover Books on Mathematics) Lynn Arthur Steen (Author), J. Arthur Seebach Jr. (Author)

Introduction to Topology: Second Edition (Dover Books on Mathematics) Theodore W. Gamelin (Author), Robert Everist Greene (Author), Mathematics (Author)

General Topology (Dover Books on Mathematics) Stephen Willard (Author)

Topology (Dover Books on Mathematics) John G. Hocking (Author), Gail S. Young (Author), Mathematics (Author)

Topology (Undergraduate Texts in Mathematics) K. Jänich (Author), S. Levy (Translator)

I should have also noted that many undergraduate students find the transition to these subjects difficult and they want to see and do problems. It doesn't hurt to make these two also available because cost is very reasonable.

Schaums Outline of General Topology (Schaum's Outline Series) Seymour Lipschutz (Author)

Topology Problem Solver (Problem Solvers Solution Guides) The Editors of REA (Author)

Lastly, if you have a another college near you, you might also peruse their collection.

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Steen & Seebach is very good, as is Willard. I’m not very fond of Hocking & Young, but it belongs in such a collection. I’m not greatly impressed by Mendelson or by Gamelin & Greene, but they’re harmless and inexpensive. –  Brian M. Scott Sep 13 '12 at 19:17
    
$+1\;$ and a great comment by Brian M. Scott, too! –  amWhy May 19 '13 at 0:23
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This has been treated here many times before. Please see the five articles linked from the "Topology: Book recommendations" section of List of Generalizations of Common Questions.

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Elementary Topology: Problem Textbook is a not so famous excellent book of Topology.

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Differential forms in Algebraic Topology, by Bott & Tu: though it overlaps a bit with the one of Madsen & Tornehave, an excellent book.

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