which of the following statements are true?
1.every homeomorphism of the $2$-sphere to itself has a fixed point.
2.the intervals [$0,1$] and ($0,1$) are homeomorphic.
3.there exists a continuous surjective function from $S^1$ onto $\mathbb{R}$.
4.there exists a continuous surjective function from complex plane onto the non-zero reals.
my effort:
1.true as $2$-sphere is a compact set.
2.true.
3.true as the function $f(α)=re^{|iα|}$ exist.
4. no idea.
can anyone help me please.....