(1.2) Let Y = {Y,o} be a metric space. Suppose (pn) and (q,) are sequences in Y, where(9n) is a Cauchy sequence and o(pn; qn) → 0 as n → x. Show the following :(a) (Pn) is a Cauchy sequence in Y,(b) Pn + a if and only if q, → x.

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Answered: (1.2) Let Y = {Y,o} be a metric space.…

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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(1.2) Let Y = {Y,o} be a metric space. Suppose (p,) and (q,) are sequences in Y, where (9n) is a Cauchy sequence and o(Pn, 4n) → 0 as n → x. Show the following : (a) (Pn) is a Cauchy sequence in Y, (b) Pn →a if and only if q, →x.