(c) Given the set T := {(x, y) = R²: xy| ≤ 1}. Is T a compact set? Show your working. Ifyou say it is not compact, then find the smallest compact set containing T.(d) Given a metric spaceX, p>, and two compact subsets S, TE X. Prove that SUT iscompact.

Given c) T=x,y∈R2:xy≤1d) Given a metric space X,ρ and two compact subsets S,T∈X

Answered: (c) Given the set T := {(x, y) = R²:…

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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(c) Given the set T := {(x, y) = R²: |xy| ≤ 1}. Is T a compact set? Show your working. If you say it is not compact, then find the smallest compact set containing T. (d) Given a metric spaceX, p>, and two compact subsets S, TEX. Prove that SUT is compact.