EDB — 0T3

[0T3] Let \(f:ℝ →ℝ^ n\) continue; show that these two conditions are equivalent

• \(\lim _{t→∞} |f(t)|=+∞\) and \(\lim _{t→-∞} |f(t)|=+∞\);

• \(f\) is proper, i.e. for every compact \(K⊂ℝ^ n\) we have that the counterimage \(f^{-1}(K)\) is a compact of \(ℝ\).