5. State whether each of the following statements is true or false, in either case substantiate/justify. (a) Let f : Q → Q be a contraction on Q. Then by Banach’ s fixed point theorem there is a unique point x ∈ Q such that f(x) = x. (b) Let X = { x∈R : -1 < x ≤ 0 or 0 < x ≤ 1} with the usual metric. Then X is disconnected.

5. State whether each of the following statements is true or false, in either case substantiate/justify. (a) Let f : Q → Q be a contraction on Q. Then by Banach’ s fixed point theorem there is a unique point x ∈ Q such that f(x) = x. (b) Let X = { x∈R : -1 < x ≤ 0 or 0 < x ≤ 1} with the usual metric. Then X is disconnected.

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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