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Which of the following statements is TRUE?

There exists an injective continuous map $f:\mathbb R^2\rightarrow S^2$.

There exists an injective continuous map $f:S^2\rightarrow\mathbb R^2$.

There exists a nonconstant polynomial with coefficients in $\mathbb C$ but with no root in $\mathbb C$.

Every continuous map $h:T^2\rightarrow T^2$ has a fixed point.

For every continuous map $T^2\rightarrow\mathbb R^2$ there exists a pair of antipodal points $x$ and $-x$ in $T^2$ with $f(x)=f(-x)$.