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These are a few problems on functions which I could not solve.

Which of the statements are true?

  1. There is a continuous bijection from $\mathbb{R}^2$$\mathbb{R}$.
  2. There is a bijection between $\mathbb{Q}$ and $\mathbb{Q} × \mathbb{Q} $.
  3. If $f : [0; 1] → [-π,π]$ is a continuous bijection then it is a homeomorphism.

Help me please. Thank you.

1 Answers 1