Smooth structure

In differential topology, a **smooth structure** on a topological manifold is an essential concept that allows us to define the notion of differentiability for the functions and maps defined on that manifold. ### Key Concepts: 1. **Manifold**: A manifold is a topological space that locally resembles Euclidean space. More formally, it is a space that can be covered by open sets that are homeomorphic to \(\mathbb{R}^n\) for some \(n\).