The interval [0, o∞) can be expressed as A. n (an, 0) where each an is a rational number B. U(an, bn] where a, and b, is a real number C. n lan, bn] where each a, and b, is an irrational number n=1 n=D1 D. All of these
The question is based on topology.
So, we are given a closed set [0,infinity). I am able to deduce that statement A is correct (since the intersection of finite open set is open; an infinite intersection could be closed or open).
Similarly, using arbitrary union of open sets is open we could rule out statement B.
However, for statement C, we know that arbitrary intersection of closed set is closed. But the statement is false. Is it because the numbers are irrational?
Please explain how to intuitively arrive at answers to such questions and provide a proof for statement A.
Please correct my reasoning for the same. I sincerely request the expert to provide a methodology using which answers to such questions could be deduced easily (atleast for real number line). Thank you.
![33. The interval [0, 0) can be expressed as
A. n (an, 00) where each a, is a rational number
B. U (an, bn] where an and b, is a real number
C. n lan, ba] where each a, and b, is an irrational number
n=1
n=1
n=D1
D. All of these](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f4412a-18c0-4f64-8bcf-4dffb42656da%2F0e72ddba-00a6-418a-a656-81ec045ec00c%2Fnwhz2zq_processed.png&w=3840&q=75)
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