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Math Help - connected spaces

  1. #1
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    connected spaces

    I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?
    Last edited by TXGirl; May 17th 2008 at 05:44 PM.
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  2. #2
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    Quote Originally Posted by TXGirl View Post
    I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?
    No. Hint: think of konstant functions.
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  3. #3
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    yes!!

    Quote Originally Posted by TXGirl View Post
    I know that the image of a connected space under a continuous map is connected, but what do you guys think about the pre-image of a connected space (still assuming a continuous map), is it necessarily connected?
    Yes the pre-image has to be connected else the image would not be connected.
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