# Math Help - connected set

1. ## 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

2. If you recall the definitions of limes superior and limes inferior, prove $L=[{\rm liminf}_{\infty}f,{\rm limsup}_{\infty}f]$.