Homotopy Type Theory modulus of Cauchy convergence > history (Rev #3)

Definition

Let $R$ be a dense integral subdomain of the rational numbers $\mathbb{Q}$ and let $R_{+}$ be the positive terms of $R$. Let $S$ be a $R_{+}$-premetric space, and let $x:I \to S$ be a net with index type $I$. A $R_{+}$-modulus of Cauchy convergence is a function $M: R_{+} \to I$ with a type

The composition $x \circ M$ of a net $x$ and a $R_{+}$-modulus of Cauchy convergence $M$ is also a net.

See also

• limit of a net
• premetric space
• Cauchy structure
• Cauchy approximation
• HoTT book real numbers

References

• Auke B. Booij, Analysis in univalent type theory (pdf)

• Univalent Foundations Project, Homotopy Type Theory – Univalent Foundations of Mathematics (2013)