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Math Help - connected set

  1. #1
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    connected set

    let f(x)be continuous on [ 0,\infty ). Define L=\{z\in R \ni \exists a sequence  x_n \rightarrow \infty and f(x_n) \rightarrow z as n \rightarrow \infty\}
    Prove a) L is closed b) L is connected c) L is an interval
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  2. #2
    Super Member Rebesques's Avatar
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    If you recall the definitions of limes superior and limes inferior, prove L=[{\rm liminf}_{\infty}f,{\rm limsup}_{\infty}f].
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