Editing Meagre set (section)

{{Short description|"Small" subset of a topological space}}
In the [[Mathematics|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 set|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 [[Sigma-ideal|σ-ideal]] of subsets; that is, any subset of a meagre set is meagre, and the [[union (set theory)|union]] of [[Countable set|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]].