dense set in a sentence

Examples

1. The importance of antichains in forcing is that for most purposes, dense sets and maximal antichains are equivalent.
2. More generally, a topological space is called ?-resolvable if it contains ? pairwise disjoint dense sets.
3. More precisely, the complement of a nowhere dense set is a set with " dense interior ".
4. This yields the fundamental identity for a dense set of invertible elements, so it follows in general by continuity.
5. On, for a dense set of, the pair is equivalent to with " b " invertible.
6. The Baire category theorem says : If " X " is a countably many nowhere dense sets is empty.
7. I believe my intuition was right : it is possible to separate two disjoint dense sets, provided both are countable.
8. Then a relatively dense set " X " is a Meyer set if and only if it is harmonious.
9. By the Schwarz reflection principle . " f " can be extended to a conformal map between these open dense sets.
10. A set is called " comeager " or " residual " if it contains the intersection of a countable family of open dense sets.