Homotopy Type Theory axiom R-flat > history (Rev #1, changes)

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Definition

Axiom $R\flat$: For a space $A$, $A$ is discrete if and only if $const: A \to (\mathbb{R} \to A)$ is an equivalence, where $\mathbb{R}$ is the Dedekind real numbers.

See also

• contractibility of Dedekind real numbers
• Dedekind real numbers

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)