Meagre set

In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is a countable union of subsets that are not dense in any non-empty open set. Thus meager sets are, in a sense, "small", being small unions of small subsets.

The meagre subsets of a fixed space form a σ-ideal of subsets; that is, any subset of a meagre set is meagre, and the union of countably many meagre sets is meagre.

Meagre sets play an important role in the formulation of the notion of Baire space and of the Baire category theorem, which is used in the proof of several fundamental results of functional analysis.

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