# Connected point sets proof

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Prove whether the following is true or false. If it is false give a counter example.

If F is a collection, each element of which is a connected point set and each point set in F contains a limit point of every other point set in F, then UF is connected.

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##### Solution Summary

This solution contains a proof regarding connected point sets.

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True.

Now suppose it is not true, that UF is not connected. Let C and D form a separation of UF. Choose a given set F_alpha from F. We know it is connected, so it either lies entirely within C or entirely within D. Without loss ...

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