These are a few problems on functions which I could not solve.
Which of the statements are true?
- There is a continuous bijection from $\mathbb{R}^2$ → $\mathbb{R}$.
- There is a bijection between $\mathbb{Q}$ and $\mathbb{Q} × \mathbb{Q} $.
- If $f : [0; 1] → [-π,π]$ is a continuous bijection then it is a homeomorphism.
Help me please. Thank you.