The collection of graph coordinate charts on \( \mathbb{S}^n \) is a real analytic atlas on \( \mathbb{S}^n \), and it defines a real analytic structure on \( \mathbb{S}^n \). This is called the standard analytic structure on \( \mathbb{S}^n \).
The collection of graph coordinate charts on \( \mathbb{S}^n \) is a real analytic atlas on \( \mathbb{S}^n \), and it defines a real analytic structure on \( \mathbb{S}^n \). This is called the standard analytic structure on \( \mathbb{S}^n \).