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Let (X, d) be a metric space and B = S(xo,r) be the open ball with centre at xo E X and radius r> 0. Show that d(B) < 2r, where d(B) denotes the diameter of the set B. Give an example to show that in general the equality may not hold in d(B) < 2r.

Let (X, d) be a metric space and B = S(xo,r) be the open ball with centre at xo E X and radius r> 0. Show that d(B) < 2r, where d(B) denotes the diameter of the set B. Give an example to show that in general the equality may not hold in d(B) < 2r.

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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Let (X, d) be a metric space and B = S(xo,r) be the open ball with centre at xo E and radius r > 0. Show that d(B) < 2r, where d(B) denotes the diameter of the set B. Give an example to show that in general the equality may not hold in d(B) < 2r.
Transcribed Image Text:Let (X, d) be a metric space and B = S(xo,r) be the open ball with centre at xo E and radius r > 0. Show that d(B) < 2r, where d(B) denotes the diameter of the set B. Give an example to show that in general the equality may not hold in d(B) < 2r.
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