Descriptive set theory | General topology

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 small or negligible in a precise sense detailed below. A set that is not meagre is called nonmeagre, or of the second category. See below for definitions of other related terms. 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. (Wikipedia).

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Uniform convergence | Topological space | Fσ set | Baire category theorem | Lebesgue measure | Countable set | Functional analysis | Isolated point | Intersection (set theory) | T1 space | Gδ set | Complement (set theory) | Banach–Mazur game | Baire space | Sigma-ideal | Complete metric space | Cofiniteness | General topology | Mathematics | Union (set theory) | Negligible set | Subset | Interior (topology) | Nicolas Bourbaki | Subspace topology | Discrete space | Cantor set | Open set