Homotopy Type Theory Topology > history (Rev #9)

Here we collect articles about doing topology in HoTT.

• cohesive homotopy type theory
• space?s and homotopy types
• discrete space?
• indiscrete space?
• underlying homotopy type?
• fundamental homotopy type?
• shape
• flat?
• sharp?
• axiom R-flat (theorem if we assume I-flat)
• real cohesive homotopy type theory?
• geometrically contractible space
• contractibility of Dedekind real numbers
• continuous mapping
• discontinuous mapping?
• intermediate value theorem
• continuous interval object?
• compact connected space

Dedekind real numbers

• frame
• sigma-frame
• extended Dedekind cut
• Dedekind real unit interval
• axiom I-flat?
• contractibility of Dedekind real unit interval?

to be moved

• Dedekind cut
• Dedekind real numbers
• Dedekind cut structure
• Dedekind cut structure real numbers
• interval cut
• Dedekind real closed intervals
• Dedekind complete Archimedean ordered field
• Dedekind complete Archimedean ordered integral domain
• an axiomatization of the real numbers