Topological Completion

The topological completion $C$ of a Field $F$ with respect to the Absolute Value $\vert\cdot\vert$ is the smallest Field containing $F$ for which all Cauchy Sequences or rationals converge.

References

Burger, E. B. and Struppeck, T. ``Does $\sum_{n=0}^\infty {1\over n!}$ Really Converge? Infinite Series and $p$-adic Analysis.'' Amer. Math. Monthly 103, 565-577, 1996.