Homotopy Type Theory axiom R-flat > history (Rev #3)

Definition

Axiom $\mathbb{R}\flat$: For a space $A$, $A$ is discrete if and only if for every universe $\mathcal{U}$ and every locally $\mathcal{U}$-small Dedekind real numbers $\mathbb{R}_\mathcal{U}$, the function $const: A \to (\mathbb{R}_\mathcal{U} \to A)$ is an equivalence.

See also

• contractibility of Dedekind real numbers
• Dedekind real numbers
• intermediate value theorem

References

• Mike Shulman, Brouwer’s fixed-point theorem in real-cohesive homotopy type theory, Mathematical Structures in Computer Science Vol 28 (6) (2018): 856-941 (arXiv:1509.07584, doi:10.1017/S0960129517000147)