Topology: A First Course, 2/e
James Munkres, Massachusetts Institute of Technology
Coming January, 2000 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 544 pp.
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For a senior undergraduate or first year graduate-level
course in Introduction to Topology. Appropriate for a one-semester
course on both general and algebraic topology or separate courses
treating each topic separately.
This text is designed to provide instructors with a convenient
single text resource for bridging between general and algebraic
topology courses. Two separate, distinct sections (one on general,
point set topology, the other on algebraic topology) are each suitable
for a one-semester course and are based around the same set of basic,
core topics. Optional, independent topics and applications can be
studied and developed in depth depending on course needs and preferences.
NEWGreatly expanded, full-semester coverage
of algebraic topologyExtensive treatment of the fundamental
group and covering spaces. What follows is a wealth of applicationsto
the topology of the plane (including the Jordan curve theorem), to
the classification of compact surfaces, and to the classification
of covering spaces. A final chapter provides an application to group
Advanced topicsSuch as metrization and imbedding
theorems, function spaces, and dimension theory are covered after
connectedness and compactness.
- Follows the present-day trend in the teaching of topology
which explores the subject much more extensively with one semester
devoted to general topology and a second to algebraic topology.
Order of topics proceeds naturally from the familiar
to the unfamiliarBegins with the familiar set theory, moves
on to a thorough and careful treatment of topological spaces, then
explores connectedness and compactness (with their many ties to calculus
and analysis), and then branches out to the new and different topics
One-or two-semester coverageProvides separate,
distinct sections on general topology and algebraic topology.
- Carefully guides students through transitions
to more advanced topics being careful not to overwhelm them. Motivates
students to continue into more challenging areas.
Many examples and figuresExploits six basic counterexamples
- Each of the text's two parts is suitable for a one-semester
course, giving instructors a convenient single text resource for bridging
between the courses. The text can also be used where algebraic topology
is studied only briefly at the end of a single-semester course.
ExercisesVaried in difficulty from the routine
to the challenging. Supplementary exercises at the end of several
chapters explore additional topics.
- Avoids overemphasis on weird counterexamples.
- Deepen students' understanding of concepts and theorems
just presented rather than simply test comprehension. The supplementary
exercises can be used by students as a foundation for an independent
research project or paper.
I. GENERAL TOPOLOGY.
1. Set Theory and Logic.
2. Topological Spaces and Continuous Functions.
3. Connectedness and Compactness.
4. Countability and Separation Axioms.
5. The Tychonoff Theorem.
6. Metrization Theorems and Paracompactness.
7. Complete Metric Spaces and Function Spaces.
8. Baire Spaces and Dimension Theory.
II. ALGEBRAIC TOPOLOGY.
9. The Fundamental Group.
10. Separation Theorems.
11. The Seifert-van Kampen Theorem.
12. Classification of Surfaces.
13. Classification of Covering Spaces.
14. Applications to Group Theory.