I've some problems concerning this question: 

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> Are the following sets compact in $C\_{[0, 1]}$ where $ d(x(t), y(t))=\sup\_{[0,1]}|x(t)-y(t)|$:
>  $${\{x(t) \mid x(t)=e^{t-a}, a>0\}},~~{ \{ x(t) \mid t^{\alpha}(1-t)^{\alpha}, \alpha>1 \}}$$
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