A metric space $(M,d)$ is called complete, a Cauchy space or Cauchy complete space if every Cauchy sequence of points of $M$ has a limit in $M$.
A Cauchy sequence is a sequence $\{x_i\}\subset M$ such that for every $\epsilon>0$ there is a index $N$ such that for $n,m\geq N$ we have
$$ d(x_n,x_m)<\epsilon $$________________________________________
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Author of the notes: Antonio J. Pan-Collantes
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