Definition
Given a topological space X, a subset A of X is meagre if it can be expressed as the union of countably many nowhere dense subsets of X. Dually, a comeagre set is one whose complement is meagre, or equivalently, the intersection of countably many sets with dense interiors.
A subset B of X is nowhere dense if there is no neighbourhood on which B is dense: for any nonempty open set U in X, there is a nonempty open set V contained in U such that V and B are disjoint.
The complement of a nowhere dense set is a dense set, but not every dense set is of this form. More precisely, the complement of a nowhere dense set is a set with dense interior.
Read more about this topic: Meagre Set
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