q*****g
发帖数: 1568 | 1 Denote {Q_i}= all rational numbers on [0,1].
Denote B_i = (Q_i-r_i, Q_i+r_i), where r_i= 1/2^(i+1).
i=1,2,.....
Let C=I\union of all B_i's, then C is a close set with
measure less than 3/4 but greater than 1/2.
Since the union of all B_i's contains all rational numbers,
the interior of C must be empty. |
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