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Suppose that X is a compact Hausdorff space. Suppose that {A} is a chain of closed connected sets. Show that the intersection of all A

Suppose that X is a compact Hausdorff space. Suppose that {A} is a chain of closed connected sets. Show that the intersection of all A is a compact connected set. This collection being a chain means that for any 1 and 2, either A1 A2 or A2 A1 .

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