# Do you know topology? 2 "Analysis Situs"

**Discrete Mathematics**Level 3

Let the sphere \(\mathbb{S}^2 = \{(x,y,z) \in \mathbb{R}^3 ; x^2 + y^2 + z^2 =1 \}\) and the torus \(\mathbb{T}^2 = \{(x,y,z) \in \mathbb{R}^3 ; (\sqrt{x^2 + y^2} - a)^2 + z^2 = r^2 \text{and } a > r >0\}\).

**Which statements below are true?**

a) There exists an homeomorphism from \(\mathbb{S}^2 \) to \(\mathbb{T}^2\)

b) There exists an homeomorphism from \(\mathbb{S}^2 \) to \(\mathbb{R}^2\)

**Details and assumptions**:

The topology used in each space is the euclidean topology