Homotopy Type Theory Cauchy real numbers (disambiguation) > history (Rev #3, changes)

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Disambiguation page

There are many different types which are called Cauchy real numbers in the literature. These include:

• sequential Cauchy real numbers?, which is defined using Cauchy sequences of a dense integral subdomain of the rational numbers.

• generalized Cauchy real numbers , which is defined using all Cauchy nets of a dense integral subdomain of the rational numbers in a universe.nets of a dense integral subdomain of the rational numbers in a universe.

• modulated sequential Cauchy real numbers? and modulated generalized Cauchy real numbers?, where the modulus of convergence is structure rather than mere property

• HoTT real numbers?, which is defined as the free complete metric space generated by a dense integral subdomain of the rational numbers, and called the Cauchy real numbers in the HoTT book.

See also

• real numbers for other types of real numbers

  real numbers for other types of real numbers

• premetric space

References

HoTT book

• Auke B. Booij, The HoTT reals coincide with the Escardó-Simpson reals, (abs:1706.05956)
• Auke B. Booij, Extensional constructive real analysis via locators, (abs:1805.06781)
• Auke B. Booij, Analysis in univalent type theory (pdf)