Cauchy sequence
Let "X" and "Y" be metric spaces, and let "f" be a function from "X" to "Y". Then "f" is Cauchy-continuous if and only if, given any Cauchy sequence ("x"1, "x"2, …) in "X", the sequence ("f"("x"1), "f"("x"2), …) is a Cauchy sequence in "Y".