In the mathematical fields of general topology and descriptive set theory, a meagre set (also called a meager set or a set of first category) is a set that, considered as a subset of a (usually larger) topological space, is in a precise sense small or negligible. The meagre subsets of a fixed space form a sigma-ideal of subsets; that is, any subset of a meagre set is meagre, and the union of countably many meagre sets is meagre.
General topologists use the term Baire space to refer to a broad class of topological spaces on which the notion of meagre set is not trivial (in particular, the entire space is not meagre). Descriptive set theorists mostly study meagre sets as subsets of the real numbers, or more generally any Polish space, and reserve the term Baire space for one particular Polish space.
The complement of a meagre set is a comeagre set or residual set.
Read more about Meagre Set: Definition, Terminology, Properties, Banach–Mazur Game
Famous quotes containing the words meagre and/or set:
“We know of no scripture which records the pure benignity of the gods on a New England winter night. Their praises have never been sung, only their wrath deprecated. The best scripture, after all, records but a meagre faith. Its saints live reserved and austere. Let a brave, devout man spend the year in the woods of Maine or Labrador, and see if the Hebrew Scriptures speak adequately to his condition and experience.”
—Henry David Thoreau (1817–1862)
“When you set out for Ithaca
ask that your way be long.”
—Constantine Cavafy (1863–1933)