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. Let A and B be two connected subset

. Let A and B be two connected subset

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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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