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=rcise 7. a) For any metric space show that B₁(x, r) C Int (Ba(x,r)). ind an appropriate metric space (X, d) for which we can find x = X and 0 such that Int(Sa(x,r)) ‡ Ø, where Sa(x, r) = {y ≤ X | d(x, y) = r}. ind an appropriate metric space (X, d) for which we can find x € X and 0 such that Ba(x, r) ‡ Int(B₁(x,r)).

=rcise 7. a) For any metric space show that B₁(x, r) C Int (Ba(x,r)). ind an appropriate metric space (X, d) for which we can find x = X and 0 such that Int(Sa(x,r)) ‡ Ø, where Sa(x, r) = {y ≤ X | d(x, y) = r}. ind an appropriate metric space (X, d) for which we can find x € X and 0 such that Ba(x, r) ‡ Int(B₁(x,r)).

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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Need parts A, B and C

Exercise 7. a) For any metric space (X, d), show that B₁(x, r) C Int(Ba(x,r)). b) Find an appropriate metric space (X, d) for which we can find x = X and r> 0 such that Int(S₁(x,r)) ‡ Ø, where Sa(x, r) = {y ≤ X | d(x, y) = r}. c) Find an appropriate metric space (X, d) for which we can find x = X and r>0 such that Ba(x, r) ‡ Int(Ba(x,r)). 2
Transcribed Image Text:Exercise 7. a) For any metric space (X, d), show that B₁(x, r) C Int(Ba(x,r)). b) Find an appropriate metric space (X, d) for which we can find x = X and r> 0 such that Int(S₁(x,r)) ‡ Ø, where Sa(x, r) = {y ≤ X | d(x, y) = r}. c) Find an appropriate metric space (X, d) for which we can find x = X and r>0 such that Ba(x, r) ‡ Int(Ba(x,r)). 2
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