Topology

Topology This introduction to topology provides separate in depth coverage of both general topology and algebraic topology Includes many examples and figures GENERAL TOPOLOGY Set Theory and Logic Topological

  • Title: Topology
  • Author: James R. Munkres
  • ISBN: 9780131816299
  • Page: 411
  • Format: Hardcover
  • This introduction to topology provides separate, in depth coverage of both general topology and algebraic topology Includes many examples and figures GENERAL TOPOLOGY Set Theory and Logic Topological Spaces and Continuous Functions Connectedness and Compactness Countability and Separation Axioms The Tychonoff Theorem Metrization Theorems and paracompactness CompleThis introduction to topology provides separate, in depth coverage of both general topology and algebraic topology Includes many examples and figures GENERAL TOPOLOGY Set Theory and Logic Topological Spaces and Continuous Functions Connectedness and Compactness Countability and Separation Axioms The Tychonoff Theorem Metrization Theorems and paracompactness Complete Metric Spaces and Function Spaces Baire Spaces and Dimension Theory ALGEBRAIC TOPOLOGY The Fundamental Group Separation Theorems The Seifert van Kampen Theorem Classification of Surfaces Classification of Covering Spaces Applications to Group Theory For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    One thought on “Topology”

    1. After making my way through Dover's excellent Algebraic Topology and Combinatorial Topology (sadly out of print), I was recommended this on account of its 'clean, accessible' (1) layout, and its wise choice of 'not completely dedicating itself to the Jordan (curve) theorem'. (2)I found it to be an even better approach to the subject than the Dover books. That said, they're all highly recommended. However, one new(er) to the concepts of algebraic and general topology will probably find this book [...]

    2. Overrated and outdated. Truth be told, this is more of an advanced analysis book than a Topology book, since that subject began with Poincare's Analysis Situs (which introduced (in a sense) and dealt with the two functors: homology and homotopy). 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. To that end, Munkres' book is a waste of time. There is not much point in getting los [...]

    3. it's not so bad, i judt hate topology a lot. This boom pretends to be a nice introduction book, but it is almost impossible to understand without a teacher or some online topology lectures

    4. rough book to get through and it doesn't motivate the concepts of a topological space right away from metric spaces, but this is a minor oversight and doesn't really detract from the book's strengths. i haven't read this book in a while so i can't really give a detailed account about it's strengths and weaknesses, but there's a reason why it's a standard text in most universities here in the united states. i recommend the reader to supplement this text with mendelson's topology text, which i bel [...]

    5. Finished the 1st half of the book (i.e. the stuff before Chapter 40). Munkres is pretty lucidly written for the most part, contains somewhat interesting exercises. Not too keen about how countability axioms were introduced (e.g. how do you demonstrate something possesses a countable basis? You need to demonstrate that this countable basis generates a topology that is finer than the topology that the set currently possesses. This is not made clear. Also, his decision to refer to it as a "basis" i [...]

    6. This book contains a great introduction to topology (more point-set than algebraic). I must admit, I have not read all of the first part of the book, but Munkres certainly makes it easier for a beginner to accept and understand the seemingly over-abstract definitions involved in point-set topology.

    7. I think this might be the best math text book ever written.I learned Topology from this book. This book is THE text to learn topology from. This book is a rare combination in that it teaches the material very well and it can be used as a reference later.The treatment on algebraic topology later in the book is a little light.

    8. This is *the* topology book for self-study. Extremely clear, full of examples. Assumes no background and gets *very* far: on the "general topology" front, does Uryssohn and Nagata-Smirnov metrization, Brouwer fixed-point, dimension theory, manifold embeddings. There's a huge section on algebraic topology which I've only skimmed, but looks similarly thorough.

    9. Delightfully clear exposition and rigorous proofs. The exercises vary from simple applications of theorems to challenging proofs. Good, clean treatment of point-set topology and algebraic topology (the latter is somewhat light, often confined particularly to results on 2-dimensional spaces).

    10. An excellent introduction to point-set and light algebraic topology. If this is your first exposure to topology, I would recommend Kinsey's "Topology of Surfaces" as a companion of solid applications in the specific case of compact 2-dimensional topology.

    11. If you need to learn point-set topology this is the place to do it. I can't vouch for all of the AT material in the latter half, but I imagine it is as good as the rest of the book. If only all texts were this clear.

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