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Simmons' Topology and Modern Analysis

  1. Nov 13, 2006 #1
    I am looking at an independent study next semester and I want to do something with point-set topology and analysis, so I have been looking at the book Introduction to Topology and Modern Analysis by Simmons, which I have heard good things about. For a little background I am currently taking Advanced Calculus and we are using Terrence Tao's Analysis I book, so I know a little analysis, but we are doing everything in the real line, nothing in metric/topological spaces. The question I must ask is how much should I try to cover in a 16-week semester? I am thinking the first 7 chapters [Sets and Functions, Metric Spaces, Topological Spaces, Compactness, Separation, Connectedness, Approximation] (the entire section on Topology) would be plenty (I could probably cover the first chapter before the semester begins since it will be nearly all review). For those who have gone through the book, or know of it, does this seem like a good amount for a 16-week course? Either way, what would you suggest? Thanks.
     
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  3. Nov 13, 2006 #2

    mathwonk

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    i suggest having as much fun as possible, and going at an any pace you find suitable. this si not a race, and it is very lengthy. so even if you start slowly, if you enjoy yourself you may well outlast others who start more quickly.

    simmons is a good, readable, intro to basic topology used in analysis. i recommend it. i liked it myaelf when i found other books like rudin too dry and repellant. if you plan to be a topologist you might like a book with less dry, more fun topology, like artin and braun.
     
  4. Nov 13, 2006 #3
    i never understood the point of topology. volume of this=volume of that?

    at least it has more applications than fractal geometry
     
  5. Nov 13, 2006 #4

    mathwonk

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    geez. get on the train. you have a great adventure ahead of you.
     
  6. Nov 13, 2006 #5

    JasonRox

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    I'm really liking Topology by Munkres. Not sure where that ranks though.
     
  7. Nov 14, 2006 #6
    If you want clearness, i suggest Munkres.
    If you want motivation, I suggest Janich, but this book does not define many things. Please be ware.
     
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