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Cont image of connected space is connected proof check?

  1. Jul 5, 2013 #1
    I was wondering if someone can tell me if my approach to the proof is a correct one. (rather than typing it all out here and making a mess of the notation, I typed it up in latex and did a screencap then put that on imgur, so the following link has the proof)

    http://i.imgur.com/gNFToKx.png
     
  2. jcsd
  3. Jul 5, 2013 #2
    It's a good proof.

    You could have simplified a lot of the notation by working with the subspace topology on ##A## and ##f(A)##. This would have simplified the question to: let ##f:X\rightarrow Y## be surjective, then if ##X## is connected then ##Y## is connected. The proof should then be the same as you gave, but the notation would be easier.
     
  4. Jul 5, 2013 #3
    Thanks so much! I will incorporate this change
     
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