# day 5

$$\def\Real{\mathbb{R}}$$

#### Topological inference

From data to simplicial complexes, A: Dowker’s theorem

From data to simplicial complexes, B: Čech and Vietoris-Rips complexes

Approximation results: finite samples from a manifold approximate the manifold well, in case of Čech complexes, thanks to Niyogi-Smale-Weinberger and in case of Vietoris-Rips complexes, thanks to Hausmann-Latschev