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Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.
That is, the nowhere dense sets form an ideal of sets, a suitable notion of negligible set.
The union of countably many nowhere dense sets, however, need not be nowhere dense.
( Thus, the nowhere dense sets need not form a sigma-ideal.
) Instead, such a union is called a meagre set or a set of first category.
The concept is important to formulate the Baire category theorem.

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