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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.

****) 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.

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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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.
Transcribed Image Text: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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