Let $\displaystyle (X,d)$ be a compact metric space, and let $\displaystyle T: X \longrightarrow X$ be a continuous map satisfying the expansion property:

$\displaystyle d(T(x),T(y)) \geq d(x,y)$ for all $\displaystyle x,y \in X$.Prove that T is surjective.

Hey I've difficulty starting this question. How do I go about doing it?

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