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Proposition 9: Every nonempty open set is the disjoint union of a countable collection of open intervals. Using Proposition 9 to write a non empty open set & as the disjoint countable union. = (akibk) k=1 Prove that it is closed then we must have Ox=-∞o and if I bk=00 for every k, so that + = IR (and there is though this is inelevant. only. Hint: The answer is the empty set and R! one b

Proposition 9: Every nonempty open set is the disjoint union of a countable collection of open intervals. Using Proposition 9 to write a non empty open set & as the disjoint countable union. = (akibk) k=1 Prove that it is closed then we must have Ox=-∞o and if I bk=00 for every k, so that + = IR (and there is though this is inelevant. only. Hint: The answer is the empty set and R! one b

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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Proposition: Every nonempty open set is the disjoint union of a countable collection of open intervals. Using Proposition 9 to write a non empty disjoint countable union. open bk=00 though this is inelevant. Hint:) The answer 0-1 (akibk) k=1 Prove that it is closed then we must have on=-∞o and if O for every k, so that + = IR (and there is only one k. set the is the empty set and R!
Transcribed Image Text:Proposition: Every nonempty open set is the disjoint union of a countable collection of open intervals. Using Proposition 9 to write a non empty disjoint countable union. open bk=00 though this is inelevant. Hint:) The answer 0-1 (akibk) k=1 Prove that it is closed then we must have on=-∞o and if O for every k, so that + = IR (and there is only one k. set the is the empty set and R!
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