. Let A and B be two connected subset
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Chapter2: Second-order Linear Odes
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Transcribed Image Text:6. Let A and B be two connected subsets of X and An B + 4. Show that AUB is connected. In
R (eqquiped with the Euclidean metric), find if the union of A = {(x,y): x? + y? < 1} and
B = {(x,y): (x – 2)2 + y? < 1} is connected or not? Justify.
Let (X, d) be a compact metric space and let d, be the metric on X defined by
d, (x, y) = min{ 1, d(x, y)},
х,у EX
Then prove that (X, d1) is compact.
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