Property of Baire

A subset ${\displaystyle A}$ of a topological space ${\displaystyle X}$ has the property of Baire (Baire property, named after René-Louis Baire), or is called an almost open set, if it differs from an open set by a meager set; that is, if there is an open set ${\displaystyle U\subseteq X}$ such that ${\displaystyle A\bigtriangleup U}$ is meager (where ${\displaystyle \bigtriangleup }$ denotes the symmetric difference).