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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- CSIR NET
- Mathematical Sciences
arbitrary collection of disjoint open intervals is countable...
This statement is wrong. Here's a counter - example. The union of countable family of open intervals (- n , n) is R which is uncountable. By Lindelof theorem, an arbitrary union of open sets can be reduced to a countable union. Therefore, if a union of a countable family of open intervals is uncountable, then a union of an uncountable super-family of open intervals can be uncountable. QED can somebody throw light on the above paragraph.....
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Sahil
the statement was:arbitrary collection of disjoint open intervals is countable.....
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Ujjawal vishal![best-answer]()
i think statement is true... and your example is not the collection of disjoint sets