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If [tex]\text C_{1} , C_{2} , C_{3}[/tex] are all non empty compact sets in [tex]\text R^n[/tex] such that [tex]\text C_{k+1} \subset C_{k} [/tex] for all k=1,2,3,......., then the set [tex]\text C = I_{k=1}^{\infty}C_{k} [/tex] is also non-empty.

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# Tough proving question

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