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Math Help - Continuous functions

  1. #1
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    Continuous functions

    Which of the following statements are true about the open interval (0,1) and the closed interval [0,1]?

    1. There is a continuous function from (0,1) onto [0,1].
    2. There is a continuous function from [0,1] onto (0,1).
    3. There is a continuous one-to-one function from (0,1) onto [0,1].

    How to prove or disprove each choice?
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  2. #2
    Senior Member roninpro's Avatar
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    Maybe I can give a a hint: continuous functions preserve compactness.
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