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Math Help - problems in analysis

  1. #1
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    problems in analysis

    - true or false:
    every compact set in R(p) is connected in R(p)


    - find an example of a function is uncontinuous at x in it is domin but it has a limit at x

    - f: R--------> R continuous proof that f([2,3]) is compact set in R

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  2. #2
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    Quote Originally Posted by nice rose View Post
    - true or false:
    every compact set in R(p) is connected in R(p)


    What is R(p)?

    - find an example of a function is uncontinuous at x in it is domin but it has a limit at x

    f(x):= \left\{\begin{array}{cc}1&\,\mbox{if } x\neq 0\\0&\,\mbox{if } x=0\end{array}\right.


    - f: R--------> R continuous proof that f([2,3]) is compact set in R

    Continuous functions map intervals to intervals, and by boundness of f it must be that f([2,3]) is a bounded interval. Now, just prove (using limits, say) that this interval is actually closed and there you are .

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  3. #3
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    What is R(p)?

    in lR p space
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