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.© BrainMass Inc. brainmass.com March 4, 2021, 5:37 pm ad1c9bdddf
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 ...
This solution contains a proof regarding connected point sets.