does it exist a dense vitali set on [0 , 1]?

Asked Feb 23 '23 at 08:51

Active Feb 23 '23 at 08:51

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We know that a vitali set may not be dense on [0, 1] according to:

now my question is that:

does it exist a dense vitali set on [0 , 1]?

asked Feb 23 '23 at 08:51

3

Yes, when you do not try to choose your representatives in a special manner, you will end up with a dense vitali set. However, to do this rigorously, you should do some things like take a countable basis of the topology of $\mathbb{R}$ and then choose one representative in each of these open sets or something. – student91 Feb 23 '23 at 09:31

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