| 1. | The complement of a nowhere dense set is a dense set.
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| 2. | The complement of a nowhere dense set is a dense set.
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| 3. | A continuous function is determined by its values on a dense set.
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| 4. | A nowhere dense set is always dense in itself.
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| 5. | In addition there is a dense set of constructible angles of infinite order.
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| 6. | Not every dense set has a nowhere dense complement.
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| 7. | The complement of a dense set can have nowhere dense, and dense regions.
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| 8. | You've discovered how to create an open dense set of arbitrarily small measure.
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| 9. | Whether all \ aleph _ 1-dense sets are order-isomorphic is independent of ZFC.
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| 10. | First, TE edited an article to say in effect that nowhere dense sets have zero measure.
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