Cont image of connected space is connected proof check?

  • #1
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Main Question or Discussion Point

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
 

Answers and Replies

  • #2
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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.
 
  • #3
125
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Thanks so much! I will incorporate this change
 

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