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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$-almost periodic functions in ${ℝ}^n,$ slowly oscillating functions in ${ℝ}^n,$ and further analyze the recently introduced class of quasi-asymptotically $c$-almost periodic functions...