nLab sequentially Cauchy-complete space

Definition

Let $S$ be a Cauchy space (such as a uniform space or a metric space). $S$ is sequentially Cauchy-complete if every Cauchy sequence in $S$ converges.

Note that this is usually just called Cauchy complete space in some areas of mathematics.

Examples

• The Dedekind real numbers are sequentially Cauchy complete.

See also

• Cauchy space
• complete space
• modulated Cauchy complete space

References

• Auke B. Booij, Analysis in univalent type theory (pdf)
• Univalent Foundations Project, Homotopy Type Theory – Univalent Foundations of Mathematics (2013)