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Let $a=(a_k)$ be a fixed element of the metric space $l_p$, where $l_p$ is equipped with its usual metric. I need to prove that the function $f:{l_p} \rightarrow {l_p}$ defined by $f:{(x_k)}\mapsto({5x_k}+{a_k})$ is continuous. Is is uniformly continuous?

Can anyone help?

Can anyone help?

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