The topological completion 
of a field 
with respect to the absolute
value 
is the smallest field containing 
for which all Cauchy sequences
or rationals converge.
Topological Completion
Explore with Wolfram|Alpha
References
Burger, E. B. and Struppeck, T. "Does
Really Converge? Infinite Series and
-adic
Analysis." Amer. Math. Monthly 103, 565-577, 1996.Referenced on Wolfram|Alpha
Topological CompletionCite this as:
Weisstein, Eric W. "Topological Completion." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TopologicalCompletion.html