Complete Metric Space

A complete metric space is a metric space in which every Cauchy sequence is convergent to a point of the space.

Examples include the real numbers with the usual metric, the complex numbers with the usual metric, and finite-dimensional real and complex vector spaces with metrics induced by norms. Further examples are the L²-space on , with functions identified when equal almost everywhere and with the L²-norm, and the p-adic numbers with their usual metric.