a) If A and B are connected in R and A B 0, prove that A U B is connected b) If Ea aA is a collection of connected sets in R and aAEa 0, prove that is connected c) If A and B are connected in R and A B , prove that A B is connected d) Show that part c) is no longer true if R2 replaces R E UE

Question: a) If A and B are connected in R and A B 0, prove that A U B is connected. b) If {Ea}aA

a) If A and B are connected in R" and A ˆ© B ‰ 0, prove that A U B is connected.
b) If {Ea}aˆˆA is a collection of connected sets in R" and ˆ©aˆˆAEa ‰ 0, prove that

is connected.
c) If A and B are connected in R and A ˆ© B ‰ Î¸, prove that A ˆ© B is connected.
d) Show that part c) is no longer true if R2 replaces R.

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