# Do you know topology? 2 "Analysis Situs"

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

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