## distance between points in two disjoint Compact sets [closed]

let $S$ and $T$ be two disjoint compact nonempty sets. Show that there are points $x_0$ in $S$ and a point $y_0$ in $T$ such that |$x$−$y$|≥|$x_0$−$y_0$| whenever $x$ is in $S$ and $y$ is in $T$.

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