Topology: 2nd edition

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These graduate courses vary on a semester-by-semester basis and are taught by Professors Gabai, Ozsvath and Szabo. What follows is a wealth of applications—to the topology of the plane (including the Jordan curve theorem), to the classification of compact surfaces, and to the classification of covering spaces. This intuition is captured by the notion of the fundamental group, which, (very) loosely speaking, is an algebraic object that counts the number of “holes” of a topological space.

Math 131: Introduction to Topology 1 - Harvard University Math 131: Introduction to Topology 1 - Harvard University

Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences. A couple of cheap, but good, books are Point Set Topology by Gaal and Topology for Analysis by Wilansky. The final part of the course is an introduction to the fundamental group π1; after some initial calculations (including for the circle), more general tools such as covering spaces and the Seifert-van Kampen theorem are used for more complicated spaces. The author spends a fifth of the book on set theory and logic, which might not be necessary for the graduate student, hence, this is probably aimed as a last year subject for an undergraduate student. This course is an introduction to algebraic topology, and has been taught by Professor Peter Ozsvath for the last few years.In particular, I think the section on coverings and fundamental group to be quite good as a reference (or to learn about for the first time).

Munkres (2000) Topology with Solutions | dbFin Munkres (2000) Topology with Solutions | dbFin

The only point of such a basic, point-set topology textbook is to get you to the point where you can work through an (Algebraic) Topology text at the level of Hatcher. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Advanced topics—Such as metrization and imbedding theorems, function spaces, and dimension theory are covered after connectedness and compactness.Firstly I apologize if this is a bit of a soft question, it's hard for me to ask this quite concretely so I do apologize if this post doesn't seem like I'm asking something immediately.