a) If A and B are connected in R and A B 0, prove that

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 ‰  θ, prove that A ˆ© B is connected.
d) Show that part c) is no longer true if R2 replaces R.

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