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(i)LetX be a set andT,T′ two toplogies onX withT ⊂T′. What does connectedness of X in...

(i)LetX be a set andT,T′ two toplogies onX withT ⊂T′. What does connectedness of X in one topology imply about connectedness in the other?

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(ii) Let X be an infinite set. Show that X is connected in the cofinite topology.

(iii) Let X be an infinite set with the cocountable topology. What can you say about the connectedness of X?

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