nLab sequentially Cauchy-complete space

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Contents

Context

Analysis

Constructivism, Realizability, Computability

Contents

Definition
Examples
See also
References

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

References

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

Last revised on November 30, 2022 at 17:59:40. See the history of this page for a list of all contributions to it.