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Math Help - Studying for upcoming test...

  1. #1
    Junior Member
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    Oct 2009
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    Hello everyone! I have a test coming up, and the attached file is a list of questions that was given to us for study purposes. I typed them on Latex to better understand them. The question though, I am wondering if anyone would like to take the time to help me prepare for my test by helping with these practice questions. Thank you!!

    Another big help would be if anyone knows of any useful sites or books for studying this kind of material would also be greatly appreciated!
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    Last edited by mr fantastic; November 9th 2009 at 06:53 PM. Reason: Merged posts
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  2. #2
    Member
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    For #2 let U\subset \mathbb{R}^2 be an open disk about the origin. Then if you remove 3 points from U it is still connected (this is because it is still path connected). Thus it's image under any continuous function is also connected (that is an interval).
    But what happens to the image after these 3 points are removed? You should reach a contradiction.
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