Uniformly Cauchy sequence
= Uniformly Cauchy sequence
{wiki=Uniformly_Cauchy_sequence}
A sequence \\((x_n)\\) in a metric space (or more generally, in a uniform space) is called a **uniformly Cauchy sequence** if for every positive real number \\(\\epsilon > 0\\), there exists a positive integer \\(N\\) such that for all indices \\(m, n \\geq N\\), the distance between the terms \\(x_m\\) and \\(x_n\\) is less than \\(\\epsilon\\).