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A briefing of Topology's most important definitions and results?

  1. Oct 5, 2013 #1
    I just need to know the basic ideas of topology, and the most important results, because I'll have differential geometry the next semester. Does anyone have a good material for this? Or you can just say what to search for and I'll search it. Thank you :)
     
  2. jcsd
  3. Oct 5, 2013 #2
    You really should understand topology pretty well before you do differential geometry. I found Munkres to be a good start, if you want to look for it. I happen to know that there are a couple copies wandering the internet.

    The basics:

    A topology, which I shall call ##\mathscr{T}##, on a space ##S## is a collection of sets contained in ##S## such that the following are satisfied:

    1. ##S## and ##\emptyset## are in ##\mathscr{T}##
    2. The union of elements in any subcollection of ##\mathscr{T}## is in ##\mathscr{T}##
    3. The intersection of elements in any finite subcollection of ##\mathscr{T}## is in ##\mathscr{T}##

    Elements of the topology are called open sets. A pairing ##(S,\mathscr{T})## is called a topological space.
     
  4. Oct 5, 2013 #3

    mathman

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    I disagree somewhat. My first exposure to differential geometry did not require any topology. The main prerequisites would be linear algebra and calculus.
     
  5. Oct 5, 2013 #4
  6. Oct 5, 2013 #5
    Chapters 2-4 of Lee, Topological Manifolds might be useful.
     
    Last edited: Oct 6, 2013
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