## Definition ## Axiom: The [[shape]] of $\mathbb{R}$ is [[contractible]]: $$p:isContr(\esh(\mathbb{R}))$$ This axiom can be derived from [[axiom R-flat]] ## See also ## * [[axiom R-flat]] * [[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](https://arxiv.org/abs/1509.07584), [doi:10.1017/S0960129517000147](https://doi.org/10.1017/S0960129517000147))