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
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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