Cantor Intersection Theorem: Let (Q₁ Q2 Qn.) be a countable collection of non-empty sets in the*****)Euclidean space IR" such that:(1) Qk+1QkV k=1,2,...;(2) Qk is closed, v k = 1,2,... and;(3) Q₁ is bounded..Then the intersection 1 Qk is closed and non-empty.

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Answered: ****) Cantor Intersection Theorem: Let…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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****) Cantor Intersection Theorem: Let (Q₁ Q2 Qn.) be a countable collection of non-empty sets in the Euclidean space IR" such that: (1) Qk+1Qk. V k=1,2,...; (2) Qk is closed, v k = 1,2,... and; (3) Q₁ is bounded. Then the intersection 1 Qk is closed and non-empty.