Homotopy Type Theory Analysis > history (Rev #37)

Here we collect articles about doing analysis in HoTT.

Real analysis is about the study of convergence and limits of sequences and functions in Archimedean ordered fields and sequentially Cauchy complete Archimedean ordered fields.

…what are the necessary requirements for the existence of an inverse: that the field be sequentially Cauchy complete, as the Banach fixed point theorem used to prove the inverse function theorem requires the metric to be sequentially Cauchy complete.

Cauchy sequences

• sequence
• sequential convergence space
• limit of a sequence
• sequentially Hausdorff space
• Cauchy sequence

Real numbers

• sequentially Cauchy complete Archimedean ordered field
• real numbers
• real vector space
• real Clifford algebra
• real geometric algebra

to be moved

• an axiomatization of the real numbers

Functions

• strongly extensional function

Intervals

• open interval
• lower bounded open interval
• upper bounded open interval
• closed interval
• unit interval

References

• HoTT Book