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Let T $T$ be an algebraic torus defined over Q$\mathbb Q$, $T_infinity$ T_\infty$be its reals real points and$\pi_0(T_infinity)$\pi_0(T_\infty)$ be the group of connected components of $T_infinity$. T_\infty$. Why is the homomorphism$T(Q)\ra T(\mathbb Q)\to \pi_0(T_infinity)$pi_0(T_\infty)$ surjective?

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# A question on algebraic torus

Let T be an algebraic torus defined over Q, $T_infinity$ be its reals points and $\pi_0(T_infinity)$ be the group of connected components of $T_infinity$. Why is the homomorphism $T(Q)\ra \pi_0(T_infinity)$ surjective?

Thanks