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Is Point-set topology worth it?

  1. May 10, 2012 #1
    It's an elective, I've been told that point-set topology isn't what I think it is. That is, there isn't much geometry in the introductory class and it's mostly a review of real analysis.

    How is the difficulty of this course? What is the typical workload? Or are these contingent upon the instructor?

    How useful would it be towards a physics education? If at all?

    Thanks

    Overview Excerpt

    Urysohn lemma, Urysohn metrization theorem, Naïve set theory, Tychonoff theorem,Tietze extension theorem
     
  2. jcsd
  3. May 11, 2012 #2
    The standard texts is Munkres. Pick up the book and check out chapters 2-5. Algebraic Topology starts around Chapter 11 or 12.
     
  4. May 11, 2012 #3
    I should mention I haven't taken Real Analysis yet...
     
  5. May 11, 2012 #4
    If you haven't taken Real Analysis, you should probably wait to take Topology.
     
  6. May 15, 2012 #5
    Okay let me fill in, sorry.

    Topology is offered next year in Winter and by the time I decide to take it I will have done Real Analaysis which is offered in Fall.

    Sorry for the confusion.

    Thanks
     
  7. May 15, 2012 #6
    To see how much you will enjoy it, you can always wait till after the real analysis course is over to decide, as some basic topology is introduced there. However in terms of usefulness, it depends how much theory you want to get into. I barely had to use any so far in undergrad physics courses, but later on it does become useful. I'd say take it if you enjoy the subject. I personally think topology is super cool stuff.

    And as for difficulty, it really depends on the particular course. My course was most definitely not a "review of real analysis". We only reviewed that stuff for about 1 day.
     
  8. May 15, 2012 #7
    That course description sounds to me to very abstract and not geometric at all (my kind of course!).
     
  9. May 15, 2012 #8
    My point set topology course overlapped with real analysis a lot in the first half. I took them simultaneously though so I didn't run into the "review of real analysis" aspect. It does a few things in more detail than real analysis does (such as separability of topological spaces, Rudin only has a few exercises developing the basics of this).

    The beginning of algebraic topology is a bit more geometric/visual (fundamental groups, covering spaces, i.e. the stuff in Munkres). My topology course covered this in the second half. Although it seems like your course is not doing this, from your description.
     
  10. May 19, 2012 #9
    It depends on the book you will be using for both R analysis and Topology. If you will be using Rudin or Apostle or some other standard text in R analysis and then using Munkres for Top, I don't think the overlap will be to severe. If you will be doing graduate complex analysis or higher level algebra, algebraic top would be a great complement.
     
  11. May 19, 2012 #10

    dextercioby

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    Point set topology is the <mother> of all mathematics, but for a mathematical physicist it's better to "eat it" from a functional analysis book. If you're going to be a mathematician though, the text by Munkres is the present standard, just as Kelley was a while ago.
     
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