Question: a) Prove that the intersection of two connected sets in R is connected. Show that this is false if R is replaced by R2. b)

a) Prove that the intersection of two connected sets in R is connected. Show that this is false if R is replaced by R2.
b) Generalize part a) as follows. If {Ea}aˆˆA is an arbitrary collection of connected sets in R, then

is also connected.

N Ea

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